Nonlinear Wave Equations

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.

List of contents

Introduction.- Linear Wave functions.- Sobolev inequality with Decay.- Estimates for solutions for linear wave equation.- Estimates for composition Function.

Summary

Establishes the complete lower bound estimates of lifespan for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions
Proposes the global iteration method, which offers a unified and straightforward approach to the problems
Accompanies readers fro
m the basics to the latest advances in the field

Product details

• Authors: Tatsie Li, Tatsien Li, Yi Zhou
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2018
• EAN: 9783662572504
• ISBN: 978-3-662-57250-4
• No. of pages: 391
• Dimensions: 155 mm x 22 mm x 235 mm
• Weight: 629 g
• Illustrations: XVI, 391 p. 2 illus.
• Series: Series in Contemporary Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Optimization, Mathematics and Statistics, Partial Differential Equations, Differential calculus & equations, Difference equations, Functional equations, Difference and Functional Equations, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization