Nonlinear parabolic equations and hyperbolic-parabolic coupled systems /
This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research c...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
Chapman and Hall/CRC,
2019.
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| Series: | Pitman monographs and surveys in pure and applied mathematics ;
76 |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown. Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set. A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the first chapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences. |
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| Item Description: | Originally published: Harlow: Longman, 1995. |
| Physical Description: | 1 online resource. |
| ISBN: | 9780429154225 0429154224 9781498749640 149874964X 9781000085235 1000085236 9781000083248 1000083241 |