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Local energy decays for wave equations with time-dependent coefficients

Published online by Cambridge University Press:  22 January 2016

Hideo Tamura
Affiliation:
Department of Engineering Mathematics, Faculty of Engineering Nagoya University
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Extract

We consider the decay of the local energy for the following equation in three dimension:

(0.1) utt + but − Δu = 0

u(0, x) = f(x) and ut (0, x) = g(x).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Bloom, C. O. and Kazarinoff, N. D., Energy decays locally even if total energy grows algebraically with time, J.of Diff. Equation, 16 (1974), 352372.CrossRefGoogle Scholar
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[4] Lax, P. and Phillips, R., “Scattering Theory”, Academic Press, New York, 1967.Google Scholar
[5] Morawetz, C., Exponential decay of solutions of the wave equation, Comm. Pure Appl. Math., 19 (1966), 439444.CrossRefGoogle Scholar
[6] Strauss, W. A., Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Math., 28 (1975), 265278.CrossRefGoogle Scholar

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