Skip to main content

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 258))

  • 749 Accesses

Abstract

In this chapter we study a simple but quite interesting equation for which the initial-value problem is well-posed. The ideas which we introduce here will be used in various places throughout the book, albeit at a “higher dialectical” level. The equation is derived from physical considerations, and in the case we consider here, the solution u(x, t), may be thought of as describing the position of a vibrating string at a point x at a time t.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Smoller, J. (1983). The One-Dimensional Wave Equation. In: Shock Waves and Reaction—Diffusion Equations. Grundlehren der mathematischen Wissenschaften, vol 258. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0152-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0152-3_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-0154-7

  • Online ISBN: 978-1-4684-0152-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics