Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems

Einav, Amit; Morgan, Jeffrey J.; Tang, Bao Q.

Abstract

In this work we study global well-posedness and large time behavior for a typical reaction-diffusion system, which include degenerate diffusion, and whose nonlinearities arise from chemical reactions. We show that there is an indirect diffusion effect, i.e., an effective diffusion for the nondiffusive species which is incurred by a combination of diffusion from diffusive species and reversible reactions between the species. Deriving new estimates for such degenerate reaction-diffusion systems, we show, by applying the entropy method, that the solution converges exponentially to equilibrium, and provide explicit convergence rates and associated constants.

Citation

Einav, A., Morgan, J. J., & Tang, B. Q. (2020). Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems. SIAM Journal on Mathematical Analysis, 52(5), 4314–4361. https://doi.org/10.1137/20m1319930

• Journal Article Type: Article
• Acceptance Date: Apr 27, 2020
• Online Publication Date: Sep 17, 2020
• Publication Date: 2020-05
• Deposit Date: Nov 16, 2020
• Journal: SIAM Journal on Mathematical Analysis
• Print ISSN: 0036-1410
• Publisher: Society for Industrial and Applied Mathematics
• Volume: 52
• Issue: 5
• Pages: 4314–4361
• DOI: https://doi.org/10.1137/20m1319930
• Public URL: https://durham-repository.worktribe.com/output/1257273