Remarks on Hölder continuity for parabolic equations and convergence to global attractors
type: Item
instance of: scholarly article
title: Remarks on Hölder continuity for parabolic equations and convergence to global attractors
zbMATH Open document ID: 0969.35034
DOI: 10.1016/S0362-546X(98)00319-8
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-11-06T00:00:00Z
review text: The author considers solutions to quasilinear parabolic equations of the form \[ {\partial u\over\partial t}= \text{div}(a(x, t,u,Du))+ b(x,t,u,Du),\quad (x,t)\in\Omega\times [0,T],\tag{\(*\)} \] where \(\Omega\) is a bounded open subset of \(\mathbb{R}^N\). Both nondegenerate and degenerate diffusion terms are allowed. The `logarithmic functions' technique is used to show interior Hölder continuity of bounded weak solutions to \((*)\). The results concerning boundary regularity in case of Dirichlet or Neumann boundary conditions and convergence of the solutions to a global attractor in the uniform supremum norm are also included.
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1526186
zbMATH Keywords: quasilinear parabolic equations
zbMATH Keywords: nondegenerate and degenerate diffusion
zbMATH Keywords: interior Hölder continuity
zbMATH Keywords: boundary regularity
author: Dung Le
reviewed by: Jan W. Cholewa
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00319-8
OpenAlex ID: W1979200061
description: scientific article; zbMATH DE number 1526186