Asymptotic and other properties of a nonlinear diffusion model
type: Item
instance of: scholarly article
title: Asymptotic and other properties of a nonlinear diffusion model
zbMATH Open document ID: 0922.35076
author: S. Rionero
author: J. N. Flavin
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-10-11T00:00:00Z
review text: Let \(\Omega\in \mathbb{R}^3\) be a sufficiently smooth bounded fixed domain ensuring the validity of divergence-like theorems. The authors consider the initial-boundary value problem \[ u_t= \Delta F(u),\quad (x,t)\in\Omega\times \mathbb{R}^+, \] \[ u(x,0)= u_0(x),\quad x\in \Omega,\quad u(x,t)= u_1(x),\quad (x,t)\in \partial\Omega\times \mathbb{R}^+, \] where \(F\in C^2(\mathbb{R})\) and \(u_0\in C^2(\overline\Omega)\), \(u_i\in C(\Omega)\) \((i= 0,1)\) are assigned functions. The authors study matters relating to the asymptotic behaviour of solutions. In particular, the authors are interested in obtaining conditions on \(F\) under which each solution tends toward a steady state when \(t\to\infty\).
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1246341
zbMATH Keywords: conditions under which each solution tends toward a steady state
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6121
OpenAlex ID: W3022978420
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DOI: 10.1006/JMAA.1998.6121
description: scientific article; zbMATH DE number 1246341