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.
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© 1994 Springer Science+Business Media New York
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Smoller, J. (1994). 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/10.1007/978-1-4612-0873-0_3
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DOI: https://doi.org/10.1007/978-1-4612-0873-0_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6929-8
Online ISBN: 978-1-4612-0873-0
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