Nonlinear Wave Equations

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Nonlinear Wave Equations

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Author : Walter A. Strauss
language : en
Publisher: American Mathematical Soc.
Release Date : 1990-01-12

Nonlinear Wave Equations written by Walter A. Strauss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-12 with Mathematics categories.

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.

Nonlinear Wave Equations

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Author : Tatsien Li
language : en
Publisher: Springer
Release Date : 2017-11-23

Nonlinear Wave Equations written by Tatsien Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Mathematics categories.

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.

Lectures On Non Linear Wave Equations

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Author : Christopher Donald Sogge
language : en
Publisher:
Release Date : 2013

Lectures On Non Linear Wave Equations written by Christopher Donald Sogge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Differential equations, Linear categories.

Nonlinear Wave Equations

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Author : Yan Guo
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Nonlinear Wave Equations written by Yan Guo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.

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.

Nonlinear Wave Equations

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Author : Satyanad Kichenassamy
language : en
Publisher: CRC Press
Release Date : 1995-09-05

Nonlinear Wave Equations written by Satyanad Kichenassamy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-05 with Science categories.

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.

Nonlinear Waves In Inhomogeneous And Hereditary Media

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Author : Aleksandr Aleksandrovich Lokshin
language : en
Publisher: Springer
Release Date : 1992

Nonlinear Waves In Inhomogeneous And Hereditary Media written by Aleksandr Aleksandrovich Lokshin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.

Solitons And Nonlinear Wave Equations

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Author : Dobb RK.
language : en
Publisher:
Release Date : 1982

Solitons And Nonlinear Wave Equations written by Dobb RK. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.

Distributional Nonlinear Wave Equations

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Author : Khaled Zennir
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-01-27

Distributional Nonlinear Wave Equations written by Khaled Zennir and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-27 with Mathematics categories.

The book contains eleven chapters introduced by an introductory description. Qualitative properties for the semilinear dissipative wave equations are discussed in Chapter 2 and Chapter 3 based on the solutions with compactly supported initial data. The purpose of Chapter 4 is to present results according to the well-possednes and behavior f solutions the nonlinear viscoelastic wave equations in weighted spaces. Elements of theory of Kirchhoff problem is introduced in Chapter 5. It is introduced same decay rate of second order evolution equations with density. Chapter 6 is devoted on the original method for Well posedness and general decay for wave equation with logarithmic nonlinearities. In Chapter 7, it is investigated the uniform stabilization of the Petrovsky-Wave nonlinear coupled system. The question of well-posedness and general energy decay of solutions for a system of three wave equations with a nonlinear strong dissipation are investigated in chapter 8 using the weighied. In sofar as Chapter 9 and chapter 10 are concerned with damped nonlinear wave problems in Fourier spaces. The last Chapter 11 analysis the existence/ nonexistence of solutions for structural damped wave equations with nonlinear memory terms in Rn.

Nonlinear Waves In Inhomogeneous And Hereditary Media

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Author : Alexandr A. Lokshin
language : en
Publisher: Springer
Release Date : 1992

Nonlinear Waves In Inhomogeneous And Hereditary Media written by Alexandr A. Lokshin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.

This booklet presents a study of one-dimensional waves in solids which can be modelled by nonlinear wave equations of different types. The factorization method is the main tool in this analysis. It allows for an exact or at least asymp totic decomposition of the wave(s) under consideration in terms of first order multipliers. Chapter 1 provides a general introduction. It presents some well-known results on characteristics, Riemann invariants, simple waves, etc. The main result of Chap. 1 is Theorem 1.3.2. (Sect. 1.3.2) which establishes the possibility of exact factorization of the nonlinear wave equation EPa(a) 1 EPa _ 0 Ij(l-u- x2 with constant coefficients. This theorem permits one to construct further factor izations of more complicated wave equations which the reader will meet in the following chapters. Chapter 2 is devoted to short wave processes in inhomogeneous media, the main result being the uniform asymptotic factorization of nonlinear wave equa tions with variable coefficients and the description of corresponding single-wave processes without the usual assumption of a small wave amplitude.

Nonlinear Wave Equations

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Author : Daqian Li
language : en
Publisher:
Release Date : 2017

Nonlinear Wave Equations written by Daqian Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Calculus of variations categories.