This book is designed to present some recent results on some nonlinear parabolic-hyp- bolic coupled systems arising from physics, mechanics and material science such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. Some of the content of this book is based on research carried out by the author and his collaborators in recent years. Most of it has been previously published only in original papers,andsomeofthematerialhasneverbeenpublisheduntilnow.Therefore,theauthor hopes that the book will bene?t both the interested beginner in the ?eld and the expert. AllthemodelsunderconsiderationinChapters2-10arebuiltonnonlinearevolution equations that are parabolic-hyperbolic coupled systems of partial differential equations with time t as one of the independentvariables. This type of partial differential equations arises not only in many ?elds of mathematics, but also in other branches of science such as physics, mechanics and materials science, etc. For example, some models studied in this book, such as the compressible Navier-Stokes equations (a 1D heat conductive v- cous real gas and a polytropic ideal gas) from ?uid mechanics, and thermo(visco)elastic systemsfrommaterialsscience, are typicalexamplesof nonlinearevolutionaryequations.
It is well known that the properties of solutions to nonlinear parabolic-hyperbolic coupledsystems are very different from those of parabolicor hyperbolicequations. Since the 1970s,more andmore mathematicianshave begunto focustheir interests onthe study of local well-posedness, global well-posedness and blow-up of solutions in a ?nite time.
- ISBN10 3764388145
- ISBN13 9783764388140
- Publish Date December 2008 (first published 1 January 2008)
- Publish Status Active
- Publish Country CH
- Imprint Birkhauser Verlag AG
- Edition New ed.
- Format eBook
- Pages 472
- Language English