How hysteresis produces discontinuous patterns in degenerate reaction–diffusion systems

Article type: Research Article

Authors: Cantin, Guillaume^{; *}

Affiliations: Laboratoire des Sciences du Numérique, LS2N UMR CNRS 6004, Université de Nantes, France

Correspondence: [*] Corresponding author. E-mail: guillaume.cantin@univ-nantes.fr.

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.

Keywords: Reaction-diffusion, degenerate, discontinuous pattern, asymptotic behavior, hysteresis

DOI: 10.3233/ASY-221818

Journal: Asymptotic Analysis, vol. 133, no. 4, pp. 447-462, 2023