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Global solutions to initial value problems in nonlinear hyperbolic thermoelasticity

Seria
Rozprawy Matematyczne tom/nr w serii: 344 wydano: 1995
Zawartość
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
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
  • Institute of Mathematics and Operations Research, Military University of Technology, Kaliskiego 2, 01-482 Warszawa, Poland
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