Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity

Jerzy August Gawinecki

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1995

Abstract

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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

How to cite

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Jerzy August Gawinecki. Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1995. <http://eudml.org/doc/268568>.

@book{JerzyAugustGawinecki1995,
abstract = {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},
author = {Jerzy August Gawinecki},
keywords = {- decay estimates; nonlinear hyperbolic thermoelasticity; Radon transform},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity},
url = {http://eudml.org/doc/268568},
year = {1995},
}

TY - BOOK
AU - Jerzy August Gawinecki
TI - Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity
PY - 1995
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
KW - - decay estimates; nonlinear hyperbolic thermoelasticity; Radon transform
UR - http://eudml.org/doc/268568
ER -

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