Linear Hyperbolic Operators

Prem K. Kythe
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Prem K. Kythe: University of New Orleans, Department of Mathematics

Chapter 4 in Fundamental Solutions for Differential Operators and Applications, 1996, pp 85-116 from Springer

Abstract: 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.

Keywords: Wave Equation; Cauchy Problem; Harmonic Oscillator; Fundamental Solution; Wave Operator (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4612-4106-5_5

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