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Article Dans Une Revue Asymptotic Analysis Année : 2022

How hysteresis produces discontinuous patterns in degenerate reaction–diffusion systems

Résumé

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.
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Dates et versions

hal-03893910 , version 1 (11-12-2022)

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Guillaume Cantin. How hysteresis produces discontinuous patterns in degenerate reaction–diffusion systems. Asymptotic Analysis, 2022, pp.1-16. ⟨10.3233/ASY-221818⟩. ⟨hal-03893910⟩
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