Large time behaviour of solutions to degenerate reaction-diffusion systems

Harsha Hutridurga, Indian Institute of Technology Bombay

Speaker	Harsha Hutridurga, Indian Institute of Technology Bombay
When	Apr 08, 2025 from 04:00 PM to 05:00 PM
Where	Via zoom
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COLLOQUIUM TALK

Abstract: The objective of this talk is to illustrate how the entropy method enables us to study, in an elementary fashion, the long-time asymptotic of solutions to reaction-diffusion systems corresponding to reversible chemistry. Loosely speaking, the entropy method looks for a nonnegative Lyapunov functional (also called entropy) and its nonnegative dissipation along the flow of the given evolution equation. This is then followed by proving a certain functional inequality referred to as the entropy-entropy dissipation inequality. The method concludes by using techniques from the theory of ordinary differential equations to derive decay estimates with explicit rates of convergence. The novelty of our work is to adapt the entropy method to address degenerate reaction-diffusion systems where one of the chemical species is non-diffusive. This talk is based on a joint work with Saumyajit Das (HRI).

Speaker Bio: Harsha Hutridurga is a faculty member in the Department of Mathematics at the Indian Institute of Technology Bombay. Previously, he worked at Imperial College London and the University of Cambridge, UK. His research focuses on partial differential equations, particularly in homogenisation and kinetic theory, reactive flows, reaction-diffusion systems, transport in strong convection regime, trend to equilibrium in kinetic theory, diffusion approximations and regularity issues in kinetic theory.

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