Existence and uniqueness of solutions for a non-uniformly parabolic equation
type: Item
instance of: scholarly article
title: Existence and uniqueness of solutions for a non-uniformly parabolic equation
zbMATH Open document ID: 1012.35048
DOI: 10.1016/S0022-0396(02)00059-1
published in: Journal of Differential Equations
publication date: 2003-04-28T00:00:00Z
review text: The authors study the generalized Burgers equation \(u_t+(u^2)_x=tu_{xx},\) which is a non-uniformly parabolic equation for \(t>0.\) It is proved existence and uniqueness of classical solutions to the initial value problem of this equation with rough initial data belonging to \(L^\infty({\mathbb R}).\)
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1901939
zbMATH Keywords: generalized Burgers equation
zbMATH Keywords: rough initial data
zbMATH Keywords: classical solutions
author: Jinghua Wang
author: Gerald Warnecke
reviewed by: Lubomira Softova
MaRDI profile type: Publication
cites work: Asymptotic solutions of model equations in nonlinear acoustics
cites work: Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method
cites work: Q5520962
cites work: The Sharp Form of Oleinik's Entropy Condition in Several Space Variables
cites work: Lectures on nonlinear hyperbolic differential equations
cites work: Q5601102
cites work: Discontinuous solutions of non-linear differential equations
cites work: Q3762690
cites work: The long time asymptotics of solutions to the generalized Burgers equation
cites work: Resolution of the spherical piston problem for compressible isentropic gas dynamics via a self-similar viscous limit
cites work: Local Error Estimates for Discontinuous Solutions of Nonlinear Hyperbolic Equations
cites work: Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws
full work available at URL: s0022-0396(02)00059-1
OpenAlex ID: W2026015350
description: scientific article; zbMATH DE number 1901939