Lectures On Non Linear Wave Equations PDF Download
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| Author | : Christopher Donald Sogge |
| Publisher | : |
| Total Pages | : 224 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : |
Download Lectures on Non-linear Wave Equations Book in PDF, ePub and Kindle
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.
| Author | : Carlos E. Kenig |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 177 |
| Release | : 2015-04-14 |
| Genre | : Mathematics |
| ISBN | : 1470420147 |
Download Lectures on the Energy Critical Nonlinear Wave Equation Book in PDF, ePub and Kindle
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.
| Author | : Walter A. Strauss |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 106 |
| Release | : 1990-01-12 |
| Genre | : Mathematics |
| ISBN | : 0821807250 |
Download Nonlinear Wave Equations Book in PDF, ePub and Kindle
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.
| Author | : Michael Reed |
| Publisher | : Springer |
| Total Pages | : 134 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354038135X |
Download Abstract Non Linear Wave Equations Book in PDF, ePub and Kindle
| Author | : Lars Hörmander |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 308 |
| Release | : 1997-07-17 |
| Genre | : Mathematics |
| ISBN | : 9783540629214 |
Download Lectures on Nonlinear Hyperbolic Differential Equations Book in PDF, ePub and Kindle
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.
| Author | : Fritz John |
| Publisher | : |
| Total Pages | : 64 |
| Release | : 1990 |
| Genre | : Nonlinear wave equations |
| ISBN | : 9781470421557 |
Download Nonlinear Wave Equations, Formation of Singularities Book in PDF, ePub and Kindle
This is the second volume in the new University Lecture series designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher Lectures presented by Fritz John in April 1989.
| Author | : Tatsien Li |
| Publisher | : Springer |
| Total Pages | : 399 |
| Release | : 2017-11-23 |
| Genre | : Mathematics |
| ISBN | : 3662557258 |
Download Nonlinear Wave Equations Book in PDF, ePub and Kindle
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
| Author | : Reinhard Racke |
| Publisher | : Birkhäuser |
| Total Pages | : 315 |
| Release | : 2015-08-31 |
| Genre | : Mathematics |
| ISBN | : 3319218735 |
Download Lectures on Nonlinear Evolution Equations Book in PDF, ePub and Kindle
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.
| Author | : Roger K. Dodd |
| Publisher | : |
| Total Pages | : 650 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : |
Download Solitons and Nonlinear Wave Equations Book in PDF, ePub and Kindle
| Author | : Lokenath Debnath |
| Publisher | : Cambridge University Press |
| Total Pages | : 372 |
| Release | : 2009-01-08 |
| Genre | : Mathematics |
| ISBN | : 0511868618 |
Download Nonlinear Waves Book in PDF, ePub and Kindle
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
