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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
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