The book is comprised of five chapters that feature the following:
. A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications.
. Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability
. Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime
. Geometric and diffractive optics, including wave interactions
. Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity
. Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations.
Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable.
- Review of new results in the area
- Continuation of previous volumes in the handbook series covering evolutionary PDEs
- New content coverage of DE applications
Large time behaviour of solutions to PDE's (A. Miranville, S. Zelik)
Cahn-Hiliard Equation (A. Novick-Cohen) Mathematical theory of viscoelastic fluids (M. Renardy)
Theory of functional parabolic equations (L. Simon
Hydrodynamical limists (A. Vasseur)
Theory of Korteweg-de Vries equation (A. Wazwaz)