Stability Technique for Evolution Partial Differential Equations

• Introduction: A Stability Approach and Nonlinear Models.- Stability Theorem: A Dynamical Systems Approach.- Nonlinear Heat Equations: Basic Models and Mathematical Techniques.- Equation of Superslow Diffusion.- Quasilinear Heat Equations with Absorption. The Critical Exponent.- Porous Medium Equation with Critical Strong Absorption.- The Fast Diffusion Equation with Critical Exponent.- The Porous Medium Equation in an Exterior Domain.- Blow-up Free-Boundary Patterns for the Navier-Stokes Equations.- The Equation ut = uxx + uln2u: Regional Blow-up.- Blow-up in Quasilinear Heat Equations Described by Hamilton-Jacobi Equations.- A Fully Nonlinear Equation from Detonation Theory.- Further Applications to Second- and Higher-Order Equations.- References.- Index.

"The authors are famous experts in the field of PDEs and blow-up techniques. In this book they present a stability theorem, the so-called S-theorem, and show, with several examples, how it may be applied to a wide range of stability problems for evolution equations. The book [is] aimed primarily aimed at advanced graduate students." --Mathematical Reviews "The book is very interesting and useful for researchers and students in mathematical physics...with basic knowledge in partial differential equations and functional analysis. A comprehensive index and bibliography are given" ---Revue Roumaine de Mathematiques Pures et Appliquees