Buch, Englisch, Band 56, 377 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 604 g
Reihe: Progress in Nonlinear Differential Equations and Their Applications
A Dynamical Systems Approach
Buch, Englisch, Band 56, 377 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 604 g
Reihe: Progress in Nonlinear Differential Equations and Their Applications
ISBN: 978-1-4612-7396-7
Verlag: Birkhäuser Boston
This book introduces a new, state-of-the-art method for the study of asymptotic behavior of solutions for evolution equations. The underlying theory hinges on a new stability result, which is presented in detail; also included is a review of basic techniques---many original to the authors---for the solution of nonlinear diffusion equations. Subsequent chapters feature a self-contained analysis of specific equations whose solutions depend on the stability theorem; a variety of estimation techniques for solutions of semi- and quasilinear parabolic equations are provided as well.
With its carefully-constructed theorems, proofs, and references, the text is appropriate for students and researchers in physics and mathematics who have basic knowledge of PDEs and some prior acquaintance with evolution equations. Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear partial differential equations.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
