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

  • Hideo Tamura (a1)

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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:

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References

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[1] Cooper, J., Local decay of solutions of the wave equation in the exterior of a moving body, J. Math. Anal. Appl., 49 (1975), 130153.
[2] Copper, J. and Strauss, W. A., Energy boundness and decay of waves reflecting off a moving obstacle, India. Univ. Math. J., 25 (1976), 671690.
[3] Lax, P. and Phillips, R., Scattering Theory, Academic Press, New York, 1967.
[4] Morawetz, C., Exponential decay of solutions of the wave equation, Comm. Pure Appl. Math., 19 (1966), 439444.
[5] Morawetz, C., Decay for solutions of the exterior problem for the wave equation, Comm. Pure Appl. Math., 28 (1975), 229264.
[6] Strauss, W. A., Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Math., 28 (1975), 265278.
[7] Taylor, M. E., Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure Appl. Math., 29 (1976), 138.
[8] Wilcox, C. H., Scattering theory for the d’Aembert equation in exterior domains, Lecture notes in Math., 442, Springer-Verlag, 1975.
[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), 312325.
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The decay of the local energy for wave equations with discontinuous coefficients

  • Hideo Tamura (a1)

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