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Linear Hyperbolic Operators

In: Fundamental Solutions for Differential Operators and Applications

Author

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  • Prem K. Kythe

    (University of New Orleans, Department of Mathematics)

Abstract

The homogeneous equation for the d’Alembertian or the wave operator □ c describes, e.g., the dynamics of a vibrating string in R 1 × R +, of a drum membrane or surface of a lake in R 2 × R +,or of a sound wave in air or an electromagnetic wave in vacuum in R 3 × R +. Here c denotes the speed of sound or light. The wave equation propagates signals with velocities less than or equal to c. Unlike the diffusion equation, the wave equation is not affected by a change in the sign in the time variable, and so in this sense it is reversible.

Suggested Citation

  • Prem K. Kythe, 1996. "Linear Hyperbolic Operators," Springer Books, in: Fundamental Solutions for Differential Operators and Applications, chapter 4, pages 85-116, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4106-5_5
    DOI: 10.1007/978-1-4612-4106-5_5
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