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
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
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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