Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity

Gawinecki, Jerzy August

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Tytuł książki

Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity

Autorzy

Jerzy August Gawinecki

Seria

Rozprawy Matematyczne tom/nr w serii: 344 wydano: 1995

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Warianty tytułu

Abstrakty

EN

CONTENTS

1. Introduction..................................................................................................................................... 5
1.1. Main Theorem 1.1................................................................................................................. 8
1.2. Main Theorem 1.2................................................................................................................. 9
2. Radon transform.................................................................................................................................... 10
2.1. Definition of the Radon transform..................................................................................... 10
2.2. Basic notations and formulae............................................................................................. 16
3. $𝕃^p$-$𝕃^q$ time decay estimates for the Cauchy problem..................... 18
3.1. Matrix of fundamental solutions for linear hyperbolic thermoelasticity....................... 18
3.2. $𝕃^p$-$𝕃^q$ time decay estimates for linear hyperbolic
thermoelasticity............................................................................................................................. 25
3.3. Fundamental solution to the linear hyperbolic heat equation...................................... 31
3.4. $𝕃^p$-$𝕃^q$ time decay estimates for the linear hyperbolic
heat equation................................................................................................................................. 35
4. 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............................................................................................................. 41
5. 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............................. 45
6. 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.................................................................................................. 50
7. General remarks.................................................................................................................................... 52
References..................................................................................................................................... 54

Słowa kluczowe

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 344

Liczba stron

61

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCXLIV

Daty

wydano

1995

otrzymano

1994-03-23

poprawiono

1994-12-21

Twórcy

autor

Jerzy August Gawinecki

Institute of Mathematics and Operations Research, Military University of Technology, Kaliskiego 2, 01-482 Warszawa, Poland

Bibliografia

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Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity

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