Nonlinear ParabolicHyperbolic Coupled Systems and Their Attractors (Operator Theory: Advances and Applications, 184),Used

Nonlinear ParabolicHyperbolic Coupled Systems and Their Attractors (Operator Theory: Advances and Applications, 184),Used

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This book is designed to present some recent results on some nonlinear parabolichyp bolic coupled systems arising from physics, mechanics and material science such as the compressible NavierStokes 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. AllthemodelsunderconsiderationinChapters210arebuiltonnonlinearevolution equations that are parabolichyperbolic 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 NavierStokes 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 parabolichyperbolic coupledsystems are very different from those of parabolicor hyperbolicequations. Since the 1970s,more andmore mathematicianshave begunto focustheir interests onthe study of local wellposedness, global wellposedness and blowup of solutions in a ?nite time.

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