Analysis of weak singularities of solutions to 1-D thermoelasticity
type: Item
instance of: scholarly article
zbMATH Open document ID: 0986.35004
publication date: 2002-06-06T00:00:00Z
Mathematics Subject Classification ID: 35A21
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 1683757
zbMATH Keywords: Cauchy problem
zbMATH Keywords: semilinear hyperbolic-parabolic systems
zbMATH Keywords: propagation of singularities
zbMATH Keywords: semilinear system of equations
zbMATH Keywords: Picard iteration
author: Michael Reissig
author: Ya-Guang Wang
MaRDI profile type: Publication
title: Analysis of weak singularities of solutions to 1-D thermoelasticity
review text: The propagation of singularities of solutions to the Cauchy problem for the one-dimensional semilinear system of equations of thermoelasticity is examined . The local existence and regularity of solutions is proved under certain assumption of the smoothness of initial data. The main idea is that the weak singularities of the solution to the semilinear problem are dominated by the corresponding linear problem. New a priori estimates to the linear problem are obtained and then applied to the proof of the uniqueness and regularity of the semilinear problem. The proof uses the construction of solution sequences by the Picard iteration for the semilinear Cauchy problem.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00056].
reviewed by: Arkadi Berezovski
description: scientific article; zbMATH DE number 1683757