References & Citations
Mathematics > Analysis of PDEs
Title: Convergence to self-similar profiles in reaction-diffusion systems
(Submitted on 2 Mar 2023 (v1), last revised 6 Apr 2023 (this version, v2))
Abstract: We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate the long-time behavior. Rescaling space and time according to the parabolic scaling, we show that solutions converge exponentially to a constant profile. In the original variables these profiles correspond to asymptotically self-similar behavior describing the diffusive mixing or equilibration of the different states at infinity. Our method provides global exponential convergence for all initial states with finite relative entropy.
Submission history
From: Stefanie Schindler [view email][v1] Thu, 2 Mar 2023 15:49:33 GMT (338kb)
[v2] Thu, 6 Apr 2023 13:07:09 GMT (374kb)
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