Stability and spectral comparison of a reaction-diffusion system with mass conservation
type: Item
instance of: scholarly article
title: Stability and spectral comparison of a reaction-diffusion system with mass conservation
zbMATH Open document ID: 1395.35111
author: Evangelos Latos
author: Yoshihisa Morita
author: Takashi Suzuki
published in: Journal of Dynamics and Differential Equations
publication date: 2018-08-21T00:00:00Z
review text: The authors are concerned with the global in-time behavior of solutions to a reaction-diffusion system with mass conservation in the form \(u_t-D\Delta u=f(u,v)\), \(v_t=d\Delta v+g(u,v)\) subject to homogeneous Neumann boundary conditions in a smooth and bounded domain. The existence of a Lyapunov function is derived which allow the authors to deduce the existence of a global-in-time solution with compact orbit. The stability and instability of stationary solutions is next investigated by using the semi-unfolding-minimality property and the spectral comparison. Finally, the dynamics near the stationary solutions is qualitatively characterized by a variational function.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6921351
zbMATH Keywords: reaction diffusion system
zbMATH Keywords: mass conservation
zbMATH Keywords: cell polarity
zbMATH Keywords: global-in-time behavior
zbMATH Keywords: Lyapunov function
zbMATH Keywords: spectral comparison
MaRDI profile type: Publication
full work available at URL: s10884-018-9650-6
OpenAlex ID: W2790527311
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Wikidata QID: Q130169331
DOI: 10.1007/S10884-018-9650-6
description: scientific article; zbMATH DE number 6921351