ORCID Profile
0000-0002-1235-0636
Current Organisation
University of New England
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Publisher: Cambridge University Press (CUP)
Date: 13-10-2023
Publisher: Springer Science and Business Media LLC
Date: 04-2021
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/07070663X
Publisher: Elsevier BV
Date: 05-2017
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2012
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/130908063
Publisher: Elsevier BV
Date: 10-2019
Publisher: Springer Science and Business Media LLC
Date: 12-2007
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/070706641
Publisher: Cambridge University Press (CUP)
Date: 06-2003
DOI: 10.1017/S0004972700037229
Abstract: We consider the logistic equation − Δ u = a ( x ) u − b ( x ) u p on all of R N with possibly unbounded coefficients near infinity. We show that under suitable growth conditions of the coefficients, the behaviour of the positive solutions of the logistic equation can be largely determined. We also show that certain linear eigenvalue problems on all of R N have principal eigenfunctions that become unbounded near infinity at an exponential rate. Using these results, we finally show that the logistic equation has a unique positive solution under suitable growth restrictions for its coefficients.
Publisher: Cambridge University Press (CUP)
Date: 02-2006
DOI: 10.1017/S0004972700038685
Abstract: We consider the logistic equation −Δ u = a ( x ) u − b ( x ) u q on all of R N with a ( x )/| x | γ and b ( x )/| x | τ bounded away from 0 and infinity for all large | x |, where γ −2, τ ∈ (−∞, ∞). We show that this problem has a unique positive solution. This considerably improves some earlier results. The main new technique here is a Safonov type iteration argument. The result can also be proved by a technique introduced by Marcus and Veron, and the two different techniques are compared.
Publisher: American Mathematical Society (AMS)
Date: 27-11-2002
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2000
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2019
Publisher: IOP Publishing
Date: 09-12-2010
Publisher: WORLD SCIENTIFIC
Date: 03-2009
Publisher: Springer Science and Business Media LLC
Date: 12-04-2011
Publisher: Cambridge University Press (CUP)
Date: 1996
DOI: 10.1017/S0308210500023064
Abstract: We study the number and stability of the positive solutions of a reaction–diffusion equation pair. When certain parameters in the equations are large, the equation pair can be viewed as singular or regular perturbations of some single (or essentially single) equation problems, for which the number and stability of their solutions can be well understood. With the help of these simpler equations, we are able to obtain a rather complete understanding of the number and stability of the positive solutions for the equation pair for the cases that certain parameters are large. In particular, we obtain a fairly satisfactory description of the positive solution set of the equation pair.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 10-2005
Publisher: Springer Science and Business Media LLC
Date: 19-07-2017
DOI: 10.1007/S00285-017-1159-9
Abstract: As vectors, mosquitoes transmit numerous mosquito-borne diseases. Among the many factors affecting the distribution and density of mosquitoes, climate change and warming have been increasingly recognized as major ones. In this paper, we make use of three diffusive logistic models with free boundary in one space dimension to explore the impact of climate warming on the movement of mosquito range. First, a general model incorporating temperature change with location and time is introduced. In order to gain insights of the model, a simplified version of the model with the change of temperature depending only on location is analyzed theoretically, for which the dynamical behavior is completely determined and presented. The general model can be modified into a more realistic one of seasonal succession type, to take into account of the seasonal changes of mosquito movements during each year, where the general model applies only for the time period of the warm seasons of the year, and during the cold season, the mosquito range is fixed and the population is assumed to be in a hibernating status. For both the general model and the seasonal succession model, our numerical simulations indicate that the long-time dynamical behavior is qualitatively similar to the simplified model, and the effect of climate warming on the movement of mosquitoes can be easily captured. Moreover, our analysis reveals that hibernating enhances the chances of survival and successful spreading of the mosquitoes, but it slows down the spreading speed.
Publisher: Elsevier BV
Date: 10-2021
Publisher: Elsevier BV
Date: 12-2009
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2014
Publisher: Springer Science and Business Media LLC
Date: 12-2003
DOI: 10.1007/BF02893084
Publisher: Elsevier BV
Date: 05-2009
Publisher: Elsevier BV
Date: 09-2004
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2020
DOI: 10.3934/CPAA.2020208
Publisher: Springer Science and Business Media LLC
Date: 12-03-2022
Publisher: Springer Science and Business Media LLC
Date: 03-02-2022
Publisher: Cambridge University Press (CUP)
Date: 02-1991
DOI: 10.1017/S0004972700028896
Abstract: A new deformation lemma for functions satisfying the Palais-Smale condition on a real Banach space is obtained. This is used to deduce some critical point theorems which are extensions of some well known results.
Publisher: Elsevier BV
Date: 11-1992
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2022
DOI: 10.3934/DCDS.2021149
Abstract: style='text-indent:20px ' We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the species, but here the population dispersal is described by "nonlocal diffusion" instead of "local diffusion". We prove that such a nonlocal diffusion problem with free boundary has a unique global solution, and for models with Lotka-Volterra type competition or predator-prey growth terms, we show that a spreading-vanishing dichotomy holds, and obtain criteria for spreading and vanishing moreover, for the weak competition case and for the weak predation case, we can determine the long-time asymptotic limit of the solution when spreading happens. Compared with the single species free boundary model with nonlocal diffusion considered recently in [ xref ref-type="bibr" rid="b7" /xref ], and the two species cases with local diffusion extensively studied in the literature, the situation considered in this paper involves several new difficulties, which are overcome by the use of some new techniques.
Publisher: Elsevier BV
Date: 04-2017
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 04-2015
Publisher: WORLD SCIENTIFIC
Date: 03-2009
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 2015
DOI: 10.4171/JEMS/568
Publisher: Elsevier BV
Date: 2022
Publisher: The Mathematical Society of the Republic of China
Date: 06-2004
Publisher: Elsevier BV
Date: 07-2007
Publisher: Elsevier BV
Date: 10-2006
Publisher: Elsevier BV
Date: 07-2001
Publisher: Elsevier BV
Date: 09-2020
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2023
Publisher: Springer International Publishing
Date: 2017
Publisher: Springer Science and Business Media LLC
Date: 25-06-2021
Publisher: Elsevier BV
Date: 12-2017
Publisher: Elsevier BV
Date: 02-2006
Publisher: World Scientific Pub Co Pte Ltd
Date: 31-01-2022
DOI: 10.1142/S1664360722300018
Abstract: In this short survey, we describe some recent developments on the modeling of propagation by reaction-differential equations with free boundaries, which involve local as well as nonlocal diffusion. After the pioneering works of Fisher, Kolmogorov–Petrovski–Piskunov (KPP) and Skellam, the use of reaction–diffusion equations to model propagation and spreading speed has been widely accepted, with remarkable progresses achieved in several directions, notably on propagation in heterogeneous media, models for interacting species including epidemic spreading, and propagation in shifting environment caused by climate change, to mention but a few. Such models involving a free boundary to represent the spreading front have been studied only recently, but fast progress has been made. Here, we will concentrate on these free boundary models, starting with those where spatial dispersal is represented by local diffusion. These include the Fisher–KPP model with free boundary and related problems, where both the one space dimension and high space dimension cases will be examined they also include some two species population models with free boundaries, where we will show how the long-time dynamics of some competition models can be fully determined. We then consider the nonlocal Fisher–KPP model with free boundary, where the diffusion operator [Formula: see text] is replaced by a nonlocal one involving a kernel function. We will show how a new phenomenon, known as accelerated spreading, can happen to such a model. After that, we will look at some epidemic models with nonlocal diffusion and free boundaries, and show how the long-time dynamics can be rather fully described. Some remarks and comments are made at the end of each section, where related problems and open questions will be briefly discussed.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2017
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2019
DOI: 10.3934/DCDS.2019213
Publisher: American Mathematical Society (AMS)
Date: 02-03-2021
DOI: 10.1090/PROC/15346
Abstract: We show that for a monostable, bistable or combustion type of nonlinear function f ( u ) f(u) , the Stefan problem \[ { a m p u t − Δ u = f ( u ) , u 0 a m p a m p for x ∈ Ω ( t ) ⊂ R n + 1 , a m p u = 0 and u t = μ | ∇ x u | 2 a m p a m p for x ∈ ∂ Ω ( t ) , \left \{ \begin {aligned} & u_t-\Delta u=f(u),\ u & & \text {for}~~x\in \Omega (t)\subset \mathbb {R}^{n+1},\\ & u=0~\text {and}~u_t=\mu |\nabla _x u|^2 & & \text {for}~~x\in \partial \Omega (t), \end {aligned} \right . \] has a traveling wave solution whose free boundary is Λ \Lambda -shaped, and whose speed is κ \kappa , where κ \kappa can be any given positive number satisfying κ κ ∗ \kappa \kappa _* , and κ ∗ \kappa _* is the unique speed for which the above Stefan problem has a planar traveling wave solution. To distinguish it from the usual traveling wave solutions, we call it a semi-wave solution. In particular, if α ∈ ( 0 , π / 2 ) \alpha \in (0, \pi /2) is determined by sin α = κ ∗ / κ \sin \alpha =\kappa _*/\kappa , then for any finite set of unit vectors { ν i : 1 ≤ i ≤ m } ⊂ R n \{\nu _i: 1\leq i\leq m\}\subset \mathbb R^n , there is a Λ \Lambda -shaped semi-wave with traveling speed κ \kappa , with traveling direction − e n + 1 = ( 0 , . . . , 0 , − 1 ) ∈ R n + 1 -e_{n+1}=(0,...,0, -1)\in \mathbb {R}^{n+1} , and with free boundary given by a hypersurface in R n + 1 \mathbb {R}^{n+1} of the form \[ x n + 1 = ϕ ( x 1 , . . . , x n ) = Φ ∗ ( x 1 , . . . , x n ) ) + O ( 1 ) as | ( x 1 , . . . , x n ) | → ∞ , x_{n+1}=\phi (x_1,..., x_n)=\Phi ^*(x_1,...,x_n))+O(1)\text { as }|(x_1,..., x_n)|\to \infty , \] where \[ Φ ∗ ( x 1 , . . . , x n ) ≔ − [ max 1 ≤ i ≤ m ν i ⋅ ( x 1 , . . . , x n ) ] cot α \Phi ^*(x_1,..., x_n)\colonequals - \left [\max _{1\leq i\leq m} \nu _i\cdot (x_1,..., x_n)\right ]\cot \alpha \] is a solution of the eikonal equation | ∇ Φ | = cot α |\nabla \Phi |=\cot \alpha on R n \mathbb R^n .
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 06-2022
DOI: 10.1137/21M1451920
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 10-2019
Publisher: Springer Science and Business Media LLC
Date: 2009
Publisher: Elsevier BV
Date: 06-2004
Publisher: Elsevier BV
Date: 08-2012
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 1999
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2022
DOI: 10.3934/MINE.2023041
Publisher: Elsevier BV
Date: 09-2007
Publisher: Elsevier BV
Date: 06-2011
Publisher: Wiley
Date: 08-2001
DOI: 10.1017/S0024610701002289
Abstract: We study, on the entire space ℝ N ( N [ges ] 1), the diffusive logistic equation and its generalizations. Here p 1 is a constant. Problem (1.1) plays an important role in understanding various population models and some other problems in applied mathematics. When λ = 1 and p = 2, it is also known as the Fisher equation and KPP equation, due to the pioneering works of Fisher [ 8 ] and Kolmogoroff, Petrovsky and Piscounoff [ 18 ].
Publisher: Elsevier BV
Date: 04-2020
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2022
DOI: 10.3934/ERA.2022016
Publisher: WORLD SCIENTIFIC
Date: 03-2009
DOI: 10.1142/7016
Publisher: Springer Science and Business Media LLC
Date: 23-04-2019
DOI: 10.1007/S00285-019-01363-2
Abstract: The purpose of this paper is to determine the precise asymptotic spreading speed of the virus for a West Nile virus model with free boundary, introduced recently in Lin and Zhu (J Math Biol 75:1381-1409, 2017), based on a model of Lewis et al. (Bull Math Biol 68:3-23, 2006). We show that this speed is uniquely defined by a semiwave solution associated with the West Nile virus model. To find such a semiwave solution, we firstly consider a general cooperative system over the half-line [Formula: see text], and prove the existence of a monotone solution by an upper and lower solution approach we then establish the existence and uniqueness of the desired semiwave solution by applying this method together with some other techniques including the sliding method. Our result indicates that the asymptotic spreading speed of the West Nile virus model with free boundary is strictly less than that of the corresponding model in Lewis et al. (2006).
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/070684173
Publisher: Elsevier BV
Date: 06-2018
Publisher: Elsevier BV
Date: 10-2004
Publisher: Springer Science and Business Media LLC
Date: 14-09-2020
Publisher: Cambridge University Press
Date: 14-02-2013
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2010
DOI: 10.1137/090775105
Publisher: Elsevier BV
Date: 07-2010
Publisher: Elsevier BV
Date: 07-2002
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/13091628X
Publisher: Elsevier BV
Date: 12-1996
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2013
DOI: 10.1137/110822608
Publisher: Elsevier BV
Date: 07-1994
Publisher: Springer Science and Business Media LLC
Date: 04-2016
DOI: 10.1007/BF03377406
Publisher: Elsevier BV
Date: 04-2015
Publisher: Springer Science and Business Media LLC
Date: 12-09-2023
Publisher: Elsevier BV
Date: 05-2002
Publisher: Elsevier BV
Date: 08-2020
Publisher: AIP Publishing
Date: 07-2005
DOI: 10.1063/1.1938747
Abstract: For type I superconductors with penetration parameter λ below a certain critical value, the existence of multiple local minimizers of the energy functional is shown. The behavior of these minimizers is examined when the Ginzburg–Landau parameter is small, and a hysteresis phenomenon is demonstrated. In contrast to the case investigated by X. B. Pan [J. Math. Phys. 44, 2639 (2003)] where λ is above the critical value, the results presented in this paper show that type I superconductors with λ below the critical value have higher critical magnetic field Hc, and exhibit more complicated superconducting behavior.
Publisher: Walter de Gruyter GmbH
Date: 05-2002
Abstract: We show that for a class of semilinear elliptic eigenvalue problems, including the model case -Δu = λu - h(x) - h(x)|u| p-1 u, u| ∂Ω = 0, where p 1 and the nonnegative function h(x) vanishes on a proper subset of Ω, global bifurcation branches from higher eigenvalues are unbounded and blow up at parameter values determined by the vanishing set Ω 0 of h(x). In particular, we prove that bifurcation from infinity is possible only at λ ∈ {λ k (Ω 0 ) : k ≥ 1}. Moreover, when Ω is an interval, for each k ≥ 1, there is a pair of continuous solution curves that bifurcate out of (λ k (Ω 0 ), ∞). For various cases, we demonstrate that there is a global bifurcation branch connecting (λ k (Ω), 0) and (λ k (Ω 0 ), ∞). Most of our results do not require the nonlinear term to be odd.
Publisher: Elsevier BV
Date: 05-2002
Publisher: World Scientific Pub Co Pte Ltd
Date: 03-12-2020
DOI: 10.1142/S0219199720500777
Abstract: In this paper, we consider a free boundary model in one space dimension which describes the spreading of a species subject to climate change, where favorable environment is shifting away with a constant speed [Formula: see text] and replaced by a deteriorated yet still favorable environment. We obtain two threshold speeds [Formula: see text] and a complete classification of the long-time dynamics of the model, which reveals significant differences between the cases [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. For ex le, when [Formula: see text], for a suitably parameterized family of initial functions [Formula: see text] increasing continuously in [Formula: see text], we show that there exists [Formula: see text] such that the species vanishes eventually when [Formula: see text], it spreads with asymptotic speed [Formula: see text] when [Formula: see text], it spreads with forced speed [Formula: see text] when [Formula: see text], and it spreads with speed [Formula: see text] when [Formula: see text]. Moreover, in the last case, while the spreading front propagates with asymptotic speed [Formula: see text], the profile of the population density function [Formula: see text] approaches a propagating pair consisting of a traveling wave with speed [Formula: see text] and a semi-wave with speed [Formula: see text].
Publisher: Informa UK Limited
Date: 04-04-2019
Publisher: Springer Science and Business Media LLC
Date: 24-08-2017
Publisher: Elsevier BV
Date: 04-1998
Publisher: American Mathematical Society (AMS)
Date: 15-06-2012
DOI: 10.1090/S0002-9947-2012-05590-5
Abstract: In this article, we study the degenerate periodic logistic equation with homogeneous Neumann boundary conditions: { ∂ t u − Δ u = a u − b ( x , t ) u p a m p in Ω × ( 0 , ∞ ) , ∂ ν u = 0 a m p on ∂ Ω × ( 0 , ∞ ) , u ( x , 0 ) = u 0 ( x ) ≥ , ≢ 0 a m p in Ω , \\begin{equation*} \\begin {cases} \\partial _t u-\\Delta u=a u-b(x,t)u^p & \\text {in $\\Omega \\times (0,\\infty )$},\\\\ \\partial _\\nu u=0 & \\text {on $\\partial \\Omega \\times (0,\\infty )$},\\\\ u(x,0) = u_0(x)\\geq , \\nequiv 0 & \\text {in $\\Omega $}, \\end{cases} \\end{equation*} where Ω ⊂ R N ( N ≥ 2 ) \\Omega \\subset \\mathbb {R}^N\\ (N\\geq 2) is a bounded domain with smooth boundary ∂ Ω \\partial \\Omega , a a and p 1 p are constants. The function b ∈ C θ , θ / 2 ( Ω ¯ × R ) b\\in C^{\\theta ,\\theta /2}(\\overline \\Omega \\times \\mathbb {R}) ( 0 θ 1 ) (0 \\theta ) is T-periodic in t t , nonnegative, and vanishes (i.e., has a degeneracy) in some subdomain of Ω × R \\Omega \\times \\mathbb {R} . We examine the effects of various natural spatial and temporal degeneracies of b ( x , t ) b(x,t) on the long-time dynamical behavior of the positive solutions. Our analysis leads to a new eigenvalue problem for periodic-parabolic operators over a varying cylinder and certain parabolic boundary blow-up problems not known before. The investigation in this paper shows that the temporal degeneracy causes a fundamental change of the dynamical behavior of the equation only when spatial degeneracy also exists but in sharp contrast, whether or not temporal degeneracy appears in the equation, the spatial degeneracy always induces fundamental changes of the behavior of the equation, though such changes differ significantly according to whether or not there is temporal degeneracy.
Publisher: The Royal Society
Date: 09-2019
Abstract: The Fisher–Kolmogorov–Petrovsky–Piskunov model, also known as the Fisher–KPP model, supports travelling wave solutions that are successfully used to model numerous invasive phenomena with applications in biology, ecology and combustion theory. However, there are certain phenomena that the Fisher–KPP model cannot replicate, such as the extinction of invasive populations. The Fisher–Stefan model is an adaptation of the Fisher–KPP model to include a moving boundary whose evolution is governed by a Stefan condition. The Fisher–Stefan model also supports travelling wave solutions however, a key additional feature of the Fisher–Stefan model is that it is able to simulate population extinction, giving rise to a spreading–extinction dichotomy . In this work, we revisit travelling wave solutions of the Fisher–KPP model and show that these results provide new insight into travelling wave solutions of the Fisher–Stefan model and the spreading–extinction dichotomy. Using a combination of phase plane analysis, perturbation analysis and linearization, we establish a concrete relationship between travelling wave solutions of the Fisher–Stefan model and often-neglected travelling wave solutions of the Fisher–KPP model. Furthermore, we give closed-form approximate expressions for the shape of the travelling wave solutions of the Fisher–Stefan model in the limit of slow travelling wave speeds, c ≪1.
Publisher: Springer Science and Business Media LLC
Date: 10-03-2018
Publisher: Springer Science and Business Media LLC
Date: 28-09-2020
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 11
DOI: 10.1137/090771089
Publisher: IOP Publishing
Date: 23-07-2020
Publisher: Elsevier BV
Date: 2008
Publisher: Cambridge University Press (CUP)
Date: 02-1993
DOI: 10.1017/S0004972700012302
Abstract: This paper is a sequel to a recent paper by the author in this journal. We prove some -variants of the min-max type critical point theorems with relaxed boundary condition and then apply the abstract results to a semilinear elliptic boundary value problem.
Publisher: Springer Science and Business Media LLC
Date: 08-01-2014
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 10-2004
Publisher: Elsevier BV
Date: 09-2003
Publisher: Indiana University Mathematics Journal
Date: 2003
Publisher: Elsevier BV
Date: 11-2013
Publisher: Springer Science and Business Media LLC
Date: 10-02-2018
Publisher: Springer Science and Business Media LLC
Date: 05-08-2021
Publisher: IOP Publishing
Date: 28-03-2023
Abstract: In this paper we establish a sharp existence result on weak traveling wave solutions for a general class of multi-species reaction–diffusion systems. Moreover, the minimal speed of the traveling waves is explicitly determined. Such a weak traveling wave solution connects the predator-free equilibrium point E 0 at x = − ∞ but needs not to connect the coexistence equilibrium E ∗ at x = ∞ . We apply this result to three important non-cooperative systems: the classical diffusive SIS system for the spread of infectious disease, a predator–prey system with age structure and a generalised Lotka–Volterra predator–prey system of one predator species feeding on n prey species, and prove with the aid of Lyapunov functions and the LaSalle invariance principle that their weak traveling wave solutions are actually traveling wave solutions that connect E ∗ at x = ∞ . For the SIS system and the generalised Lotka–Volterra predator–prey system, we develop additional techniques to establish the boundedness of their weak traveling wave solutions before applying the LaSalle’s invariance principle.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2009
Publisher: Elsevier BV
Date: 03-2009
Publisher: Elsevier BV
Date: 03-2015
Publisher: Elsevier BV
Date: 05-2013
Publisher: Elsevier BV
Date: 08-2022
Publisher: Wiley
Date: 09-12-2018
DOI: 10.1112/BLMS.12229
Publisher: Springer Science and Business Media LLC
Date: 08-08-2023
DOI: 10.1007/S00208-022-02451-3
Abstract: We study the dynamics of a population with an age structure whose population range expands with time, where the adult population is assumed to satisfy a reaction–diffusion equation over a changing interval determined by a Stefan type free boundary condition, while the juvenile population satisfies a reaction–diffusion equation whose evolving domain is determined by the adult population. The interactions between the adult and juvenile populations involve a fixed time-delay, which renders the model nonlocal in nature. After establishing the well-posedness of the model, we obtain a rather complete description of its long-time dynamical behaviour, which is shown to follow a spreading–vanishing dichotomy. When spreading persists, we show that the population range expands with an asymptotic speed, which is uniquely determined by an associated nonlocal elliptic problem over the half line. We hope this work will inspire further research on age-structured population models with an evolving population range.
Publisher: Cambridge University Press (CUP)
Date: 08-2006
DOI: 10.1017/S0308210500004704
Abstract: To understand the heterogeneous spatial effect on predator–prey models, we study the behaviour of the positive steady states of a predator–prey model as certain parameters are small or large. We compare the case when the model has a spatial degeneracy with the case when it does not have such a degeneracy. Our results show that the effect of the degeneracy can be clearly observed in one limiting case, but not in the others.
Publisher: Elsevier BV
Date: 03-2017
Publisher: Indiana University Mathematics Journal
Date: 2015
Publisher: Springer Science and Business Media LLC
Date: 10-2012
Publisher: Cambridge University Press (CUP)
Date: 04-2004
DOI: 10.1017/S0308210500003218
Abstract: For a wide class of nonlinearities f ( u ) satisfying but not necessarily Lipschitz continuous, we study the quasi-linear equation where T = { x = ( x 1 , x 2 , …, x N ) ∈ R N : x 1 0} with N ≥ 2. By using a new approach based on the weak maximum principle, we show that any positive solution on T must be a function of x 1 only. Under our assumptions, the strong maximum principle does not hold in general and the solution may develop a flat core our symmetry result allows an easy and precise determination of the flat core.
Publisher: Elsevier BV
Date: 2008
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2015
DOI: 10.1137/140994848
Publisher: IOP Publishing
Date: 18-09-2023
Publisher: American Mathematical Society (AMS)
Date: 09-2007
Publisher: Springer Science and Business Media LLC
Date: 31-05-2022
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 2010
DOI: 10.4171/JEMS/198
Publisher: Elsevier
Date: 2005
Publisher: Springer Science and Business Media LLC
Date: 25-01-2022
DOI: 10.1038/S41467-022-28148-4
Abstract: Ion currents through potassium channels are gated. Constriction of the ion conduction pathway at the inner helix bundle, the textbook gate of Kir potassium channels, has been shown to be an ineffective permeation control, creating a rift in our understanding of how these channels are gated. Here we present evidence that anionic lipids act as interactive response elements sufficient to gate potassium conduction. We demonstrate the limiting barrier to K + permeation lies within the ion conduction pathway and show that this gate is operated by the fatty acyl tails of lipids that infiltrate the conduction pathway via fenestrations in the walls of the pore. Acyl tails occupying a surface groove extending from the cytosolic interface to the conduction pathway provide a potential means of relaying cellular signals, mediated by anionic lipid head groups bound at the canonical lipid binding site, to the internal gate.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2021
Publisher: Springer Science and Business Media LLC
Date: 07-07-2015
Publisher: Wiley
Date: 23-03-2015
DOI: 10.1112/JLMS/JDV003
Publisher: Wiley
Date: 23-08-2005
Publisher: Springer Science and Business Media LLC
Date: 25-06-2013
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Yihong Du.