Nonlinear Wave Equations / by Tatsien Li, Yi Zhou.

Format:

Book

Author/Creator:

Li, Tatsien., Author.

Zhou, Yi., Author.

Series:

Series in Contemporary Mathematics, 2364-009X ; 2

Language:

English

Subjects (All):

Differential equations, Partial.

Difference equations.

Functional equations.

Calculus of variations.

Partial Differential Equations.

Difference and Functional Equations.

Calculus of Variations and Optimal Control; Optimization.

Local Subjects:

Partial Differential Equations.

Difference and Functional Equations.

Calculus of Variations and Optimal Control; Optimization.

Physical Description:

1 online resource (XVI, 391 p. 2 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017.

Summary:

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.

Contents:

Introduction

Linear Wave functions

Sobolev inequality with Decay

Estimates for solutions for linear wave equation

Estimates for composition Function.

Notes:

Includes bibliographical references and index.

ISBN:

3-662-55725-8