Asymptotic Methods For Investigating Quasiwave Equations Of Hyperbolic Type
Download Asymptotic Methods For Investigating Quasiwave Equations Of Hyperbolic Type PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Asymptotic Methods For Investigating Quasiwave Equations Of Hyperbolic Type book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type
Author: Yuri A. Mitropolsky
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The theory of partial differential equations is a wide and rapidly developing branch of contemporary mathematics. Problems related to partial differential equations of order higher than one are so diverse that a general theory can hardly be built up. There are several essentially different kinds of differential equations called elliptic, hyperbolic, and parabolic. Regarding the construction of solutions of Cauchy, mixed and boundary value problems, each kind of equation exhibits entirely different properties. Cauchy problems for hyperbolic equations and systems with variable coefficients have been studied in classical works of Petrovskii, Leret, Courant, Gording. Mixed problems for hyperbolic equations were considered by Vishik, Ladyzhenskaya, and that for general two dimensional equations were investigated by Bitsadze, Vishik, Gol'dberg, Ladyzhenskaya, Myshkis, and others. In last decade the theory of solvability on the whole of boundary value problems for nonlinear differential equations has received intensive development. Significant results for nonlinear elliptic and parabolic equations of second order were obtained in works of Gvazava, Ladyzhenskaya, Nakhushev, Oleinik, Skripnik, and others. Concerning the solvability in general of nonlinear hyperbolic equations, which are connected to the theory of local and nonlocal boundary value problems for hyperbolic equations, there are only partial results obtained by Bronshtein, Pokhozhev, Nakhushev.
Methods and Applications of Singular Perturbations
Author: Ferdinand Verhulst
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-06-04
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Averaging Methods in Nonlinear Dynamical Systems
Author: Jan A. Sanders
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-08-18
Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews