Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems
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A01=Songmu Zheng
Author_Songmu Zheng
Banach Space
Cahn-Hilliard's equations
Category=PBKJ
dynamical systems theory
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
equilibrium analysis
Equilibrium Point
Finite Fractal Dimension
fluid dynamics modeling
Global Attractor
hyperbolic-parabolic coupled systems
Inertial Manifold
Inertial Set
Infinite Dimensional Dynamical Systems
Infinitesimal Generator
Interpolation Spaces
Linear Evolution Equations
Linear Parabolic System
mathematical physics applications
nonlinear evolution equations research
nonlinear parabolic equations
Nonlinear Semigroup
nonlinear thermoelasticity
Nonlocal Terms
Nontrivial Solutions
partial differential equations
Phase Field Equations
Self-adjoint Positive Definite Operator
Separable Hilbert Space
Sobolev spaces
Sobolev's Imbedding Theorem
Sobolev’s Imbedding Theorem
Unique Global Solution
Vice Versa
Product details
- ISBN 9780367448974
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 02 Dec 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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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.
Zheng, Songmu
