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Zeitschrift für Analysis und ihre Anwendungen


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Volume 35, Issue 2, 2016, pp. 199–210
DOI: 10.4171/ZAA/1562

Published online: 2016-04-13

An Example of a Non-Trivial, Non-Self-Adjoint Huygens Differential Equation in Four Independent Variables

Stephanie R. Czapor[1] and Raymond G. McLenaghan[2]

(1) Laurential University, Sudbury, Canada
(2) University of Waterloo, Canada

A family of non-trivial, essentially non-self-adjoint wave equations which satisfy Huygens' principle is given. It is constructed on a 4-dimensional Lorentzian space which is a product of two 2-dimensional spaces of constant curvature. Prior to this example, the only known non-trivial Huygens equation was the scalar wave equation on the exact plane wave spacetime as presented by Günther.

Keywords: Initial value problem, Huygens' principle, Hadamard's problem, non-self-adjoint wave equation

Czapor Stephanie, McLenaghan Raymond: An Example of a Non-Trivial, Non-Self-Adjoint Huygens Differential Equation in Four Independent Variables. Z. Anal. Anwend. 35 (2016), 199-210. doi: 10.4171/ZAA/1562