Accession Number : ADA116324

Title :   Global Existence of Solutions of the Equations of One-Dimensional Thermoviscoelasticity with Initial Data in BV and L(1).

Descriptive Note : Technical summary rept.,


Personal Author(s) : Kim,Jong Uhn

PDF Url : ADA116324

Report Date : Apr 1982

Pagination or Media Count : 86

Abstract : This paper discusses the Cauchy problem associated with a particular system of equations of one-dimensional nonlinear thermoviscoelasticity with the initial data given in the class of functions of bounded variation (denoted by BV). It has been known that the class of BV is a suitable function space for the study of evolution equations which arise in continuum mechanics in order to admit solutions possessing shocks. This fact has been exploited in the analysis of hyperbolic conservation laws which describe the motion of a continuum when mechanical and thermal dissipations are neglected. On the other hand, only the smooth (classical) solutions have been studied for the equations which include such dissipative terms. Our goal is to study the global existence of weaker solutions of systems which include such dissipative terms. Our main result shows that when the initial data are sufficiently small in the Lagrangian form and BV norms, the system (1) of the abstract has global solutions in time possessing specific regularity properties. (Author)

Descriptors :   *Linear algebraic equations, *One dimensional, *Viscoelasticity, *Thermal properties, Hyperbolas, Lagrangian functions, Continuum mechanics, Conservation, Evolution(General), Equations, Global, Dissipation, Mechanical properties, Shock waves, Nonlinear algebraic equations, Variations

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE