Download or read book Lectures on Non linear Wave Equations written by Christopher Donald Sogge and published by . This book was released on 2008 with total page 224 pages. 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.
Download or read book Lectures on the Energy Critical Nonlinear Wave Equation written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2015-04-14 with total page 177 pages. 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.
Download or read book Nonlinear Wave Equations written by Walter A. Strauss and published by American Mathematical Soc.. This book was released on 1990-01-12 with total page 106 pages. 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.
Download or read book Abstract Non Linear Wave Equations written by Michael Reed and published by Springer. This book was released on 2006-11-14 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Nonlinear Hyperbolic Differential Equations written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 1997-07-17 with total page 308 pages. 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.
Download or read book Nonlinear Wave Equations Formation of Singularities written by Fritz John and published by . This book was released on 1990 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Solitons and Nonlinear Wave Equations written by Roger K. Dodd and published by . This book was released on 1982 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Nonlinear Evolution Equations written by Reinhard Racke and published by Birkhäuser. This book was released on 2015-08-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Waves written by Lokenath Debnath and published by Cambridge University Press. This book was released on 2009-01-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Nonlinear Waves and Shocks written by Cathleen S. Morawetz and published by . This book was released on 1981 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy and published by CRC Press. This book was released on 2021-05-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
Download or read book Nonlinear Wave Equations written by Tatsien Li and published by Springer. This book was released on 2017-11-23 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book ABSTRACT NON LINEAR WAVE EQUATIONS LECTURES FROM A PROJECT MATHEMATICAL PROBLEMS OF QUANTUM DYNAMICS ZENTRUM FUR INTERDISZIPLINARE FORSCHUNG UNIVERSITY OF BIELEFELD written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Nonlinear Evolution Equations written by Reinhard Racke and published by Vieweg+Teubner Verlag. This book was released on 2014-04-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an elementary, self contained introduction into some important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The presentation is made using the classical method of continuation of local solutions with the help of a priori estimates obtained for small data.
Download or read book Nonlinear Wave Equations written by Yan Guo and published by American Mathematical Soc.. This book was released on 2000 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents original research papers and expository articles from the conference in honour of Walter A. Strauss's 60th birthday, held at Brown University in Providence, Rhode Island. The book offers a collection of original papers and expository articles mainly devoted to the study of nonlinear wave equations. The articles cover a wide range of topics, including scattering theory, dispersive waves, classical field theory, mathematical fluid dynamics, kinetic theory, stability theory, and variational methods. The book offers a cross-section of current trends and research directions in the study of nonlinear wave equations and related topics.
Download or read book Nonlinear Waves in Inhomogeneous and Hereditary Media written by Aleksandr Aleksandrovich Lokshin and published by Springer. This book was released on 1992 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Vibrations and the Wave Equation written by Alain Haraux and published by Springer. This book was released on 2018-05-02 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987. An additional chapter has been added to reflect more recent advances in the field.
