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The decay of the local energy for wave equations with discontinuous coefficients

Published online by Cambridge University Press:  22 January 2016

Hideo Tamura
Hideo Tamura*
Affiliation:
Department of Mathematics, Faculty of Engineering, Nagoya University
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The exponential decay of the local energy for wave equations in exterior domains of the odd dimensional space has been proved in [1] ~ [6] etc. under the Dirichlet boundary condition and in [5], [7] under the Neumann condition and the other conditions. In this paper, we shall consider this problem for the following equation:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 68 , November 1977 , pp. 35 - 58
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Cooper, J., Local decay of solutions of the wave equation in the exterior of a moving body, J. Math. Anal. Appl., 49 (1975), 130–153.Google Scholar
[2] Copper, J. and Strauss, W. A., Energy boundness and decay of waves reflecting off a moving obstacle, India. Univ. Math. J., 25 (1976), 671–690.Google Scholar
[3] Lax, P. and Phillips, R., Scattering Theory, Academic Press, New York, 1967.Google Scholar
[4] Morawetz, C., Exponential decay of solutions of the wave equation, Comm. Pure Appl. Math., 19 (1966), 439–444.CrossRefGoogle Scholar
[5] Morawetz, C., Decay for solutions of the exterior problem for the wave equation, Comm. Pure Appl. Math., 28 (1975), 229–264.Google Scholar
[6] Strauss, W. A., Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Math., 28 (1975), 265–278.Google Scholar
[7] Taylor, M. E., Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure Appl. Math., 29 (1976), 1–38.CrossRefGoogle Scholar
[8] Wilcox, C. H., Scattering theory for the d’Aembert equation in exterior domains, Lecture notes in Math., 442, Springer-Verlag, 1975.CrossRefGoogle Scholar
[9] Zachmanoglou, E. C., The decay of solutions of the initial-boundary value problem for the wave equation in unbounded regions, Arch. Rat. Mech. Anal., 14 (1963), 312–325.CrossRefGoogle Scholar