Existence results of steady-states of semilinear reaction-diffusion equations and their applications
type: Item
instance of: scholarly article
title: Existence results of steady-states of semilinear reaction-diffusion equations and their applications
zbMATH Open document ID: 0685.35057
DOI: 10.1016/0022-0396(89)90146-0
author: Yanyan Li
published in: Journal of Differential Equations
publication date: 1989-01-01T00:00:00Z
review text: This paper is concerned with the asymptotic behavior of solutions to the initial boundary value problem of semilinear parabolic equation \[ u_ t=u_{xx}+f(x,u,u_ x),\quad in\quad (a,b)\times (0,\infty) \] \[ u(a,t)=h(t),u(b,t)=k(t)\quad for\quad t>0;\quad u(x,0)=g(x)\quad for\quad a\leq x\leq b. \] Using the well known Nagumo lemma, the authors prove the existence of a steady-state solution for the above problem. Some results on quenching phenomena and existence of the minimal and maximal solutions are also presented. Sufficient conditions on the initial data which give rise to the phenomena of finite-time blow-up and the decay of the solution are also given, respectively.
reviewed by: Songmu Zheng
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 4122471
zbMATH Keywords: steady-states
zbMATH Keywords: existence
zbMATH Keywords: quenching
zbMATH Keywords: blow-up
zbMATH Keywords: decay
MaRDI profile type: Publication
full work available at URL: 0022-0396(89)90146-0
OpenAlex ID: W2029767117
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description: scientific article; zbMATH DE number 4122471