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Blowup for Nonlinear Hyperbolic Equations

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 787/5 ( reviews)

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Book Synopsis Blowup for Nonlinear Hyperbolic Equations by : Serge Alinhac

Download or read book Blowup for Nonlinear Hyperbolic Equations written by Serge Alinhac. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: Solutions to partial differential equations or systems often, over specific time periods, exhibit smooth behaviour. Given sufficient time, however, they almost invariably undergo a brutal change in behaviour, and this phenomenon has become known as blowup. In this book, the author provides an overview of what is known about this situation and discusses many of the open problems concerning it.

Hyperbolic Partial Differential Equations

2009-06-17 Mathematics
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Release : 2009-06-17
Genre : Mathematics
Kind : eBook
Book Rating : 238/5 ( reviews)

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Book Synopsis Hyperbolic Partial Differential Equations by : Serge Alinhac

Download or read book Hyperbolic Partial Differential Equations written by Serge Alinhac. This book was released on 2009-06-17. Available in PDF, EPUB and Kindle. Book excerpt: This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.

Global Propagation of Regular Nonlinear Hyperbolic Waves

2009-09-01 Science
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Release : 2009-09-01
Genre : Science
Kind : eBook
Book Rating : 353/5 ( reviews)

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Book Synopsis Global Propagation of Regular Nonlinear Hyperbolic Waves by : Tatsien Li

Download or read book Global Propagation of Regular Nonlinear Hyperbolic Waves written by Tatsien Li. This book was released on 2009-09-01. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

2014-09-22 Mathematics
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Release : 2014-09-22
Genre : Mathematics
Kind : eBook
Book Rating : 736/5 ( reviews)

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Book Synopsis Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations by : Victor A. Galaktionov

Download or read book Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations written by Victor A. Galaktionov. This book was released on 2014-09-22. Available in PDF, EPUB and Kindle. Book excerpt: 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

Blow-Up in Nonlinear Equations of Mathematical Physics

2018-08-06 Mathematics
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Release : 2018-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 075/5 ( reviews)

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Book Synopsis Blow-Up in Nonlinear Equations of Mathematical Physics by : Maxim Olegovich Korpusov

Download or read book Blow-Up in Nonlinear Equations of Mathematical Physics written by Maxim Olegovich Korpusov. This book was released on 2018-08-06. Available in PDF, EPUB and Kindle. Book excerpt: The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results

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