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Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors [electronic resource] /by Yuming Qin.

by Qin, Yuming [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Operator Theory: Advances and Applications, Advances in Partial Differential Equations: 184Publisher: Basel : Birkhäuser Basel, 2008.Description: online resource.ISBN: 9783764388140.Subject(s): Mathematics | Operator theory | Differential equations, partial | Mathematics | Partial Differential Equations | Operator TheoryDDC classification: 515.353 Online resources: Click here to access online
Contents:
Preliminary -- A One-dimensional Nonlinear Viscous and Heat-conductive Real Gas -- A One-dimensional Polytropic Viscous and Heat-conductive Gas -- A Polytropic Ideal Gas in Bounded Annular Domains in -- A Polytropic Viscous Gas with Cylinder Symmetry in -- One-dimensional Nonlinear Thermoviscoelasticity -- A Nonlinear One-dimensional Thermoelastic System with a Thermal Memory -- One-dimensional Thermoelastic Equations of Hyperbolic Type -- Blow-up for the Cauchy Problem in Nonlinear One-dimensional Thermoelasticity -- Large-Time Behavior of Energy in Multi-Dimensional Elasticity.
In: Springer eBooksSummary: This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequalities in analysis, and the theory of semigroups of linear operators and of global attractors.
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Preliminary -- A One-dimensional Nonlinear Viscous and Heat-conductive Real Gas -- A One-dimensional Polytropic Viscous and Heat-conductive Gas -- A Polytropic Ideal Gas in Bounded Annular Domains in -- A Polytropic Viscous Gas with Cylinder Symmetry in -- One-dimensional Nonlinear Thermoviscoelasticity -- A Nonlinear One-dimensional Thermoelastic System with a Thermal Memory -- One-dimensional Thermoelastic Equations of Hyperbolic Type -- Blow-up for the Cauchy Problem in Nonlinear One-dimensional Thermoelasticity -- Large-Time Behavior of Energy in Multi-Dimensional Elasticity.

This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequalities in analysis, and the theory of semigroups of linear operators and of global attractors.

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