5 Ergebnisse.

Providing exact solutions of more than 200 nonlinear equations and models, this book begins with classical as well as more recent examples of interesting solutions on linear invariant subspaces for nonlinear operators. In the remainder of the book, the authors develop several techniques for constructing exact solutions that describe singularity behavior for various nonlinear PDEs, including gas dynamics models, free-boundary problems, Green-Na...

* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential 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 PDEs.* Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

This book is a reference on nonlinear second-order parabolic partial differential equations that are used as models to help solve a broad class of engineering and physical problems. The analytical ideas used are geometric as opposed to super-sub solution methods that have limited application in the physical world. Sturm Theory is the cornerstone of this type of analysis, which was developed almost two hundred years ago, but then lost or forgot...

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs. The book first studies the particular self-similar singularity solutions (patterns) of the equations. Thi...

Providing exact solutions of more than 100 nonlinear equations and models, this book begins with classical as well as more recent examples of interesting solutions on linear invariant subspaces for nonlinear operators. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including gas dynamics models, free-boundary problems, Green-Naghdi equations, and quasilinear pseu...