Affiliation:
1. Laboratoire des Sciences du Numérique, LS2N UMR CNRS 6004, Université de Nantes, France
Abstract
In this paper, we study the asymptotic behaviour of the solutions to a degenerate reaction–diffusion system. This system admits a continuum of discontinuous stationary solutions due to the effect of a hysteresis process, but only one discontinuous stationary solution is compatible with a principle of preservation of locally invariant regions. Using a macroscopic mass effect which guarantees that fast particles help slow particles to displace, we establish a novel result of convergence of a non trivial set of trajectories towards a discontinuous pattern.
Reference22 articles.
1. Approximating travelling waves by equilibria of non-local equations;Arrieta;Asymptotic Analysis,2012
2. Non-existence of the global attractor for a partly dissipative reaction–diffusion system with hysteresis;Cantin;Journal of Differential Equations,2021
3. Mathematical modeling of forest ecosystems by a reaction–diffusion–advection system: Impacts of climate change and deforestation;Cantin;Journal of Mathematical Biology,2021
4. W.A. Coppel, Stability and Asymptotic Behavior of Differential Equations, Heath, 1965.
5. Indirect diffusion effect in degenerate reaction–diffusion systems;Einav;SIAM Journal on Mathematical Analysis,2020