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Propagation of classical solutions to the perturbed wave equation in a space of odd dimension

Published online by Cambridge University Press:  14 November 2011

Gustavo Perla Menzala
Gustavo Perla Menzala
Affiliation:
Institute of Mathematics, U.F.R.J., Caixa Postal 68530, Rio de Janeiro, RJ Brasil Department of Mathematics and Division of Applied Mathematics, Brown University, Providence, RI02912, U.S.A.
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Synopsis

We prove that classical solutions of the perturbed wave equation in ℝn × ℝ (n = odd ≧ 3) do not satisfy Huygens' principle in the presence of symmetries. The difficulties arising from the singularities of the Riemann function (for large space dimensions) are overcome by considering a class of potentials and initial data which are radial and smooth. Our method is elementary and based on energy estimates.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 337 - 344
Copyright
Copyright © Royal Society of Edinburgh 1984

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