On quasilinear parabolic equations in the Orlicz spaces
type: Item
instance of: scholarly article
title: On quasilinear parabolic equations in the Orlicz spaces
zbMATH Open document ID: 1315.47081
author: Fei Fang
author: Chao Ji
published in: Nonlinear Analysis. Real World Applications
publication date: 2014-11-25T00:00:00Z
review text: The paper under review deals with quasilinear parabolic equations of the form \[ \begin{cases} u_t-\text{div\,}\big(a(|\nabla u|)\nabla u\big)=g(u), & (x,t)\in \Omega\times(0,T),\\ u(x,t)=0, & (x,t)\in \partial\Omega\times(0,T),\\ u(x,0)=u_0(x)\in L^2(\Omega), & \end{cases} \] where \(\Omega\subset \mathbb{R}^n\) is a bounded and smooth domain. The authors study the existence and asymptotic behavior of solutions in the framework of the Orlicz-Sobolev spaces via operator theory and nonlinear semigroups theory.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 6373715
zbMATH Keywords: Orlicz-Sobolev spaces
zbMATH Keywords: quasilinear parabolic equations
zbMATH Keywords: attractor
zbMATH Keywords: nonlinear semigroups
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2014.09.005
OpenAlex ID: W2009826687
cites work: Mountain pass type solutions for quasilinear elliptic equations
cites work: Existence and multiplicity of solutions for a class of quasilinear elliptic equations: an Orlicz-Sobolev space setting
cites work: On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems
cites work: Positive Solutions of Quasilinear Elliptic Equations with Critical Orlicz-Sobolev Nonlinearity on RN
cites work: On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting
cites work: Linking over cones and nontrivial solutions for \(p\)-Laplace equations with \(p\)-superlinear nonlinearity
cites work: Focusing solutions for the \(p\)-Laplacian evolution equation
cites work: Asymptotic analysis of the \(p\)-Laplacian flow in an exterior domain
cites work: A multiplicity theorem for problems with the \(p\)-Laplacian
cites work: Nontrivial critical groups in \(p\)-Laplacian problems via the Yang index
cites work: Q5318420
cites work: Q4000065
cites work: Applications of Orlicz spaces
cites work: Q5665783
cites work: Q4094029
cites work: Q4795215
cites work: Q4704642
cites work: Q3100036
cites work: Q4039920
cites work: Q3998731
cites work: Infinite-dimensional dynamical systems in mechanics and physics
cites work: Applications of B-bounded nonlinear semigroups to particle transport problems
cites work: A global attractor for a \(p(x)\)-Laplacian parabolic problem
cites work: Nonlinear semigroups and the yang-mills equations with the metallic boundary conditions
cites work: A Nonlinear semigroup approach to the navier—stokes system
cites work: Q4842674
DOI: 10.1016/J.NONRWA.2014.09.005
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description: scientific article; zbMATH DE number 6373715