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Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type : Mathematics and Its Applications - Yuri A. Mitropolsky

Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type

Mathematics and Its Applications

Hardcover Published: 30th April 1997
ISBN: 9780792345299
Number Of Pages: 214

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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.

Preface
Existence Theorems for Hyperbolic Equationsp. 1
Periodic Solutions of the Wave Ordinary Differential Equations of Second Orderp. 24
Periodic Solutions of the First Class Systemsp. 42
Periodic Solutions of the Second Class Systemsp. 60
Periodic Solutions of the Second Order Integro-Differential Equations of Hyperbolic Typep. 91
Hyperbolic Systems With Fast and Slow Variables and Asymptotic Methods for Solving Themp. 118
Asymptotic Methods for the Second Order Partial Differential Equations of Hyperbolic Typep. 161
Bibliographyp. 199
Indexp. 205
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345299
ISBN-10: 0792345290
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 214
Published: 30th April 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.4
Weight (kg): 1.1