Bound for the solution of a degenerate parabolic equation
type: Item
instance of: scholarly article
title: Bound for the solution of a degenerate parabolic equation
zbMATH Open document ID: 0724.35006
author: R. Yu. Nabokov
published in: Moscow University Mathematics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: The author studies the initial-boundary value problem for homogeneous Dirichlet data for the partial differential equation \[ Lu=u_ t- \partial_ i(a_{ij}\partial_ ju)+cu=f, \] where the elliptic part of L is allowed to degenerate. More precisely, it is assumed that \(a_{ij}\xi_ i\xi_ j\geq \nu | \xi |^ 2\), where \(\nu\) (x,t)\(\geq 0\) and \(1/\nu (\cdot,t)\in L^ p(\Omega)\) for all \(t>0\), for some \(p\geq 1\). It is stated that any solution to this problem is bounded from above by the solution to the corresponding spherically symmetrized problem.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 4194246
zbMATH Keywords: Dirichlet data
zbMATH Keywords: symmetrized problem
reviewed by: Jürgen Sprekels
MaRDI profile type: Publication
description: scientific article