Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions
type: Item
instance of: scholarly article
title: Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions
zbMATH Open document ID: 1015.35020
DOI: 10.1016/S1468-1218(02)00014-7
author: Seong-A Shim
published in: Nonlinear Analysis. Real World Applications
publication date: 2003-03-11T00:00:00Z
review text: The author proves the uniform boundedness and convergence of global solution for quasilinear parabolic systems with cross-diffusions dominated by self-diffusions in population dynamics. Applying Gagliardo-Nirenberg type inequalities, some uniform \(W_2^1\)-bounds uniform in time are established. Convergence of solutions is established for systems with large diffusion coefficients.
reviewed by: Sebastian Aniţa
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 1880145
zbMATH Keywords: quasilinear parabolic systems
zbMATH Keywords: Gagliardo-Nirenberg type inequalities
MaRDI profile type: Publication
cites work: Q4073917
cites work: Dynamic theory of quasilinear parabolic systems. III: Global existence
cites work: Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
cites work: Q4284440
cites work: An initial-boundary-value problem for a certain density-dependent diffusion system
cites work: Q5630031
cites work: Smooth solutions to a quasi-linear system of diffusion equations for a certain population model
cites work: Diffusion, self-diffusion and cross-diffusion
cites work: On the global existence of a cross-diffusion system
cites work: Q3260749
cites work: Q3856484
cites work: Q5533735
cites work: Global solution to some quasilinear parabolic system in population dynamics
description: scientific article; zbMATH DE number 1880145