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. TOC:Preface.- 1. Preliminaries.- 2. A 1D Nonlinear Viscous and Heat-conductive Real Gas.- 3. A 1D Polytropic Viscous and Heat-conductive Gas.- 4. A Polytropic Ideal Gas in Bounded Annular Domains.- 5. A Polytropic Viscous Gas with Cylinder Symmetry.- 6. 1D Nonlinear Thermoviscoelasticity.- 7. A Nonlinear 1D Thermoelastic Systems with Thermal Memory.- 8. 1D Thermoelastic Equations of Hyperbolic Type.- 9. Blow-up for the Cauchy Problem.- 10. Large-Time Behaviour of Energy in Multi-Dimensional Elasticity.- Index.
