New perspectives on nonlocal equations. This project aims at tackling cutting-edge problems in the field of mathematical analysis, with specific focus on nonlocal equations, by introducing innovative approaches and a unified perspective. It focuses on the use of long-range interactions to deeply understand new effects arising in several mathematical problems of great impact.
The research will be performed through stimulating international collaborations, providing exchange opportunities and idea ....New perspectives on nonlocal equations. This project aims at tackling cutting-edge problems in the field of mathematical analysis, with specific focus on nonlocal equations, by introducing innovative approaches and a unified perspective. It focuses on the use of long-range interactions to deeply understand new effects arising in several mathematical problems of great impact.
The research will be performed through stimulating international collaborations, providing exchange opportunities and ideal conditions for students to complete their training.
The expected outcomes include new techniques to solve difficult problems, high impact international research collaborations, training of the next generation of mathematicians and top tier journal publications.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL190100081
Funder
Australian Research Council
Funding Amount
$3,532,919.00
Summary
Minimal surfaces, free boundaries and partial differential equations. This project enhances Australia as a world leader in the field of mathematical analysis, focusing on regularity and qualitative properties of solutions of partial differential equations and nonlocal problems, and solving very challenging research questions in a key strategic area of international science.
The broad applicability of the results constitutes a very fertile ground for cross-disciplinary interactions with scientist ....Minimal surfaces, free boundaries and partial differential equations. This project enhances Australia as a world leader in the field of mathematical analysis, focusing on regularity and qualitative properties of solutions of partial differential equations and nonlocal problems, and solving very challenging research questions in a key strategic area of international science.
The broad applicability of the results constitutes a very fertile ground for cross-disciplinary interactions with scientists of other disciplines.
A new research team based in Western Australia will be founded, connecting world leaders and talented early career researchers, providing an ideal training environment for students and PostDocs, offering an excellent image of the scientific community and developing strategic fields of knowledge.Read moreRead less
Wavelet approaches for solving nonlinear dynamic systems in process engineering. The success of the proposed project will enable us to obtain more accurate numerical solutions for the nonlinear dynamical systems arising from process engineering. This ensures the potential for understanding and optimising industrial and engineering processes. Hence, a wide range of processing industries in Australia, such as agricultural chemicals, mineral processing, food, detergents, pharmaceuticals, ceramics ....Wavelet approaches for solving nonlinear dynamic systems in process engineering. The success of the proposed project will enable us to obtain more accurate numerical solutions for the nonlinear dynamical systems arising from process engineering. This ensures the potential for understanding and optimising industrial and engineering processes. Hence, a wide range of processing industries in Australia, such as agricultural chemicals, mineral processing, food, detergents, pharmaceuticals, ceramics and specialty chemicals will benefit from the results of this project. This will ensure globally competitive production and, therefore, greater contributions to the Australian economy.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100954
Funder
Australian Research Council
Funding Amount
$354,968.00
Summary
Partial Differential Equations, geometric aspects and applications. The study of Partial Differential Equations (PDEs) is a classical and prolific field of research having a fundamental role in the development of mathematical analysis and motivated by important applications in natural and applied sciences.
This project aims to obtain substantial progress in the field of PDEs. The area of mathematical research covered is extremely broad, at the confluence of analysis and geometry, and with many a ....Partial Differential Equations, geometric aspects and applications. The study of Partial Differential Equations (PDEs) is a classical and prolific field of research having a fundamental role in the development of mathematical analysis and motivated by important applications in natural and applied sciences.
This project aims to obtain substantial progress in the field of PDEs. The area of mathematical research covered is extremely broad, at the confluence of analysis and geometry, and with many applications to other areas of mathematics and natural and applied sciences. The results that will be obtained will produce a significant amount of new knowledge in this extremely difficult, but rapidly growing, field, by exploiting international scientific collaborations and interdisciplinary methods.Read moreRead less
Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concr ....Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concrete applications. This project should contribute to the development of the mathematical theory and give insight for concrete applications in physics and biology.Read moreRead less
Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical un ....Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical understanding of which outflow shapes are stable, and under what circumstances they might become unstable. This will provide valuable information about galaxy shapes, and a new suite of computational methods for solving such problems.Read moreRead less
Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods f ....Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.
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Novel nonlinear functional analysis methods for singular and impulsive boundary value problems. This project aims to develop innovative functional analysis theories and methods to study various complex nonlinear boundary value problems, with particular focus on singular and impulsive problems. The outcomes of this project aims to enhance Australia’s capability of tackling complex nonlinear science and engineering problems using sophisticated mathematical methods. This project aims to also provid ....Novel nonlinear functional analysis methods for singular and impulsive boundary value problems. This project aims to develop innovative functional analysis theories and methods to study various complex nonlinear boundary value problems, with particular focus on singular and impulsive problems. The outcomes of this project aims to enhance Australia’s capability of tackling complex nonlinear science and engineering problems using sophisticated mathematical methods. This project aims to also provide engineers and scientists with a theoretical base and simulation technique for the study and optimal control of impulsive systems and processes involving nonlinear singularity.Read moreRead less
A geometric theory for modern optimisation problems in control and estimation. Linear-quadratic and spectral factorisation problems play a crucial role in system and control theory as well as many important application areas. The success of the project will represent a significant advancement of state-of-the-art in these broad areas.
Discovery Early Career Researcher Award - Grant ID: DE180100957
Funder
Australian Research Council
Funding Amount
$339,328.00
Summary
Partial differential equations, free boundaries and applications. This project aims to investigate fundamental problems in the analysis of partial differential equations and free boundary theory, to develop advanced mathematical theories with the possibility of important applications. The expected outcome is the establishment of a regularity and classification theory for nonlocal equations and for free boundary problems in linear and nonlinear settings. The benefit of the project lies in a concr ....Partial differential equations, free boundaries and applications. This project aims to investigate fundamental problems in the analysis of partial differential equations and free boundary theory, to develop advanced mathematical theories with the possibility of important applications. The expected outcome is the establishment of a regularity and classification theory for nonlocal equations and for free boundary problems in linear and nonlinear settings. The benefit of the project lies in a concrete advancement of the mathematical research with advantages for a deeper understanding of complex phenomena in physics and biology. Some of the problems also provide results useful for industrial applications.Read moreRead less