Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics
type: Item
instance of: scholarly article
title: Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics
zbMATH Open document ID: 0963.35079
DOI: 10.1016/S0362-546X(98)00303-4
author: Ansgar Jüngel
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-06-18T00:00:00Z
review text: The author deals with the parabolic system \[ {\partial \over\partial t}\rho_i(u)+ \text{div } J_i=W_i(u,V), \quad i=1,\ldots, n, \] \[ {\partial \over \partial t}\rho_{n+1}(u)+\text{div }J_{n+1}=W_{n+1}(u,V)- \sum_{k=1}^ne_k \nabla V\cdot J_k\quad \text{in} \Omega\times(0,\tau), \] where \(\Omega\subset \mathbb{R}^d\), \(d\geq 1\) is a bounded domain and \(\tau>0.\) Under suitable conditions on the data there are proved regularity \((u\in L^\infty(H^1)\cup H^1(L^2)\), \(V\in L^\infty(W^{2,p}))\) and uniqueness results.
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 1512501
zbMATH Keywords: spatial and temporal regularity
zbMATH Keywords: uniqueness of weak solutions
zbMATH Keywords: semidiscretization of time
zbMATH Keywords: elliptic dual method
reviewed by: Lubomira Softova
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1512501