Title
Computer-Assisted Proofs for some linear and non linear reaction diffusion systems
Abstract
Multi-species diffusion reaction equations are systems with unique solving difficulties for each of them. However, thanks to computer-assisted methods, it is possible to establish properties of these equations in a systematic way.
Initially, we will focus on a non-linear cross-diffusion system and on obtaining stationary solutions to this system. One of the main difficulties is dealing with non-polynomial non-linearities. After establishing a suitable solution space and a toolbox based on Neumann series and Taylor expansions, we use a Newton-Kantorovitch Theorem to show the existence of many stationary states. We then look at a linear diffusion reaction system.We will establish the stability of the system with respect to a free parameter, by generalising a Gershgorin theorem and using an adapted Newton-Kantorovitch theorem. Finally, we look at the question of the stability of stationary states in a non-linear cross-diffusion system.
Initially, we will focus on a non-linear cross-diffusion system and on obtaining stationary solutions to this system. One of the main difficulties is dealing with non-polynomial non-linearities. After establishing a suitable solution space and a toolbox based on Neumann series and Taylor expansions, we use a Newton-Kantorovitch Theorem to show the existence of many stationary states. We then look at a linear diffusion reaction system.We will establish the stability of the system with respect to a free parameter, by generalising a Gershgorin theorem and using an adapted Newton-Kantorovitch theorem. Finally, we look at the question of the stability of stationary states in a non-linear cross-diffusion system.
Please note that the seminar will take place in person in room 144 of Huxley Building.