Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity

Jerzy August Gawinecki

GDML_Books, (1995), p.

Résumé

CONTENTS1. Introduction..................................................................................................................................... 5 1.1. Main Theorem 1.1................................................................................................................. 8 1.2. Main Theorem 1.2................................................................................................................. 92. Radon transform.................................................................................................................................... 10 2.1. Definition of the Radon transform..................................................................................... 10 2.2. Basic notations and formulae............................................................................................. 163. $^p$-$^q$ time decay estimates for the Cauchy problem..................... 18 3.1. Matrix of fundamental solutions for linear hyperbolic thermoelasticity....................... 18 3.2. $^p$-$^q$ time decay estimates for linear hyperbolic thermoelasticity............................................................................................................................. 25 3.3. Fundamental solution to the linear hyperbolic heat equation...................................... 31 3.4. $^p$-$^q$ time decay estimates for the linear hyperbolic heat equation................................................................................................................................. 354. Local existence of solutions................................................................................................................ 39 4.1. Local existence of solutions to the initial value problem for nonlinear hyperbolic thermoelasticity............................................................................................................................. 39 4.2. Local existence of solutions to the initial value problem for the nonlinear hyperbolic heat equation............................................................................................................. 415. High energy estimates......................................................................................................................... 42 5.1. High energy estimates for the nonlinear hyperbolic thermoelasticity........................ 42 5.2. High energy estimates for the nonlinear hyperbolic heat equation............................. 456. Global solutions in nonlinear hyperbolic thermoelasticity theory................................................. 46 6.1. Proof of main Theorem 1.1.................................................................................................. 46 6.2. Proof of main Theorem 1.2.................................................................................................. 507. General remarks.................................................................................................................................... 52 References..................................................................................................................................... 54

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Zbl 0844.35068

EUDML-ID : urn:eudml:doc:268568