Remarks on global bounds of solutions of parabolic equations in divergence form
type: Item
instance of: scholarly article
title: Remarks on global bounds of solutions of parabolic equations in divergence form
zbMATH Open document ID: 0676.35043
DOI: 10.1216/RMJ-1987-17-3-499
published in: Rocky Mountain Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Consider the Dirichlet problems of parabolic equations \[ (1)\quad u_ t=\sum a_ i(t,x,u,u_ x)_{x_ i}+a(t,x,u,u_ x)u+f(t,x);\quad u=0\quad on\quad \partial \Omega \subset R^ n \] and \[ (2)\quad u_ t=u_{xx}+f(t,x,u,u_ x,u_{xx},u_ t);\quad u_ x=0\quad on\quad \partial \Omega. \] In this paper some properties of solutions of (1) are proved with the proof of a variant of the maximum principle and global boundedness of the spatial derivative \(u_ x\) for (2) with bounded perturbation \(f(t,x,u,u_ x,u_{xx},u_ t)\) are studied.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 4107279
zbMATH Keywords: global bounds
zbMATH Keywords: solutions
zbMATH Keywords: parabolic equations
zbMATH Keywords: Dirichlet problems
zbMATH Keywords: maximum principle
zbMATH Keywords: global boundedness
zbMATH Keywords: bounded perturbation
author: Tomasz Dlotko
MaRDI profile type: Publication
full work available at URL: rmj-1987-17-3-499
OpenAlex ID: W1963790888
description: scientific article; zbMATH DE number 4107279