This article is cited in 4 papers

Existence of Global Weak Solutions to the Equations of One-Dimensional Nonlinear Thermoviscoelasticity with Discontinuous Data

A. A. Amosov

Moscow Power Engineering Institute (Technical University)

Abstract: The existence of global weak solutions to initial–boundary value problems for a system of quasilinear differential equations describing the dynamics of a one-dimensional Voigt-type thermoviscoelastic body is established. The initial and boundary data may be discontinuous functions. Only physically natural requirements are imposed on the data. In particular, it is required that the initial velocity and initial temperature should be such that the full energy is finite. The density of heat sources and a boundary heat flux may be functions from $L_1$. The functions defining the properties of the body may also be discontinuous in $x$.

UDC: 517.958+533.7

Received in November 2000

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 3–11

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