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Lectures on Non-linear Wave Equations

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
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Book Synopsis Lectures on Non-linear Wave Equations by : Christopher Donald Sogge

Download or read book Lectures on Non-linear Wave Equations written by Christopher Donald Sogge. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Presents an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. This book examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced.

Nonlinear Wave Equations

1990-01-12 Mathematics
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Release : 1990-01-12
Genre : Mathematics
Kind : eBook
Book Rating : 250/5 ( reviews)

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Book Synopsis Nonlinear Wave Equations by : Walter A. Strauss

Download or read book Nonlinear Wave Equations written by Walter A. Strauss. This book was released on 1990-01-12. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

Lectures on the Energy Critical Nonlinear Wave Equation

2015-04-14 Mathematics
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Release : 2015-04-14
Genre : Mathematics
Kind : eBook
Book Rating : 147/5 ( reviews)

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Book Synopsis Lectures on the Energy Critical Nonlinear Wave Equation by : Carlos E. Kenig

Download or read book Lectures on the Energy Critical Nonlinear Wave Equation written by Carlos E. Kenig. This book was released on 2015-04-14. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentration-compactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and well-posedness" conjecture (defocusing case) and the "ground-state" conjecture (focusing case) in critical dispersive problems. The second part of the monograph describes the "channel of energy" method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the three-dimensional radial focusing energy critical wave equation. It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations. A co-publication of the AMS and CBMS.

Lectures on Nonlinear Hyperbolic Differential Equations

1997-07-17 Mathematics
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Release : 1997-07-17
Genre : Mathematics
Kind : eBook
Book Rating : 214/5 ( reviews)

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Book Synopsis Lectures on Nonlinear Hyperbolic Differential Equations by : Lars Hörmander

Download or read book Lectures on Nonlinear Hyperbolic Differential Equations written by Lars Hörmander. This book was released on 1997-07-17. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.

Abstract Non Linear Wave Equations

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 35X/5 ( reviews)

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Book Synopsis Abstract Non Linear Wave Equations by : Michael Reed

Download or read book Abstract Non Linear Wave Equations written by Michael Reed. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt:

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