Skip to main content
SpringerLink
Log in

Nonlinear Wave Equations

  • Book
  • © 2017

Overview

Authors:
  1. Tatsien Li

    1. School of Mathematical Sciences, Fudan University, Shanghai, China

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Yi Zhou

    1. School of Mathematical Sciences, Fudan University, Shanghai, China

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Series in Contemporary Mathematics (SCMA, volume 2)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 59.99 USD 119.00
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99 USD 159.99
50% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 79.99 USD 159.99
50% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Introduction and Overview

    • Tatsien Li, Yi Zhou
    Pages 1-16

  3. Linear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages 17-33

  4. Sobolev Type Inequalities with Decay Factor

    • Tatsien Li, Yi Zhou
    Pages 35-64

  5. Estimates on Solutions to the Linear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages 65-111

  6. Some Estimates on Product Functions and Composite Functions

    • Tatsien Li, Yi Zhou
    Pages 113-131

  7. Cauchy Problem of the Second-Order Linear Hyperbolic Equations

    • Tatsien Li, Yi Zhou
    Pages 133-153

  8. Reduction of Nonlinear Wave Equations to a Second-Order Quasi-linear Hyperbolic System

    • Tatsien Li, Yi Zhou
    Pages 155-160

  9. Cauchy Problem of One-Dimensional Nonlinear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages 161-181

  10. Cauchy Problem of \(n({\ge }3)\)-Dimensional Nonlinear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages 183-216

  11. Cauchy Problem of Two-Dimensional Nonlinear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages 217-254

  12. Cauchy Problem of Four-Dimensional Nonlinear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages 255-262

  13. Null Condition and Global Classical Solutions to the Cauchy Problem of Nonlinear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages 263-301

  14. Sharpness of Lower Bound Estimates on the Life-Span of Classical Solutions to the Cauchy Problem—The Case that the Nonlinear Term \(F=F(Du, D_xDu)\) on the Right-Hand Side Does not Depend on u Explicitly

    • Tatsien Li, Yi Zhou
    Pages 303-317

  15. Sharpness of Lower Bound Estimates on the Life-Span of Classical Solutions to the Cauchy Problem—The Case that the Nonlinear Term \(F=F(u,Du, D_xDu)\) on the Right-Hand Side Depends on u Explicitly

    • Tatsien Li, Yi Zhou
    Pages 319-361

  16. Applications and Developments

    • Tatsien Li, Yi Zhou
    Pages 363-382

  17. Erratum to: Nonlinear Wave Equations

    • Tatsien Li, Yi Zhou
    Pages E1-E1

  18. Back Matter

    Pages 383-391
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • School of Mathematical Sciences, Fudan University, Shanghai, China

    Tatsien Li, Yi Zhou

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation