Periodic solutions for double degenerate quasilinear parabolic equations
type: Item
instance of: scholarly article
title: Periodic solutions for double degenerate quasilinear parabolic equations
zbMATH Open document ID: 1012.35050
DOI: 10.1016/S0362-546X(01)00893-8
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: This paper deals with the existence of periodic solutions for the following double degenerate quasilinear parabolic equations of the type \[ \begin{aligned} \frac{\partial(b(x)u)}{\partial t}-\sum_{i=1}^ND_iA_i(x,t,u,Du)+A_0(x,t,u)=f(x,t)&\quad\text{in }Q:=\Omega\times (0,T),\\ b(x)u(x,0)=b(x)u(x,T)&\quad\text{in }\Omega, \end{aligned} \tag{1} \] on the space \(X=L^2(0,T;V)\), where \(V=W^{1,2}_0(v,\Omega)\) is a weighted Sobolev space. The degeneration is determined by a scalar function \(b(x)\) and a vector function \(v(x)=(v_1(x),\cdots,v_N(x))\) with positive components \(v_i(x)\) in \(\Omega\) satisfying certain integrability assumptions. Under some appropriate hypothesis, the author proves the existence of periodic solution for problem (1).
reviewed by: Peixuan Weng
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1836643
zbMATH Keywords: weighted Sobolev space
zbMATH Keywords: double degeneration
zbMATH Keywords: Quasilinear parabolic equations
zbMATH Keywords: Pseudomonotone operators
zbMATH Keywords: Periodic solutions
author: Zhenhai Liu
MaRDI profile type: Publication
cites work: On the solvability of degenerated quasilinear elliptic equations of higher order
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cites work: Nonlinear degenerate parabolic equations
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full work available at URL: s0362-546x(01)00893-8
OpenAlex ID: W2095514766
description: scientific article; zbMATH DE number 1836643