On the decay of local energy for wave equations with time-dependent potentials

Hideo TAMURA

doi:10.2969/jmsj/03340605

Hideo TAMURA

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 4 Pages 605-618

DOI https://doi.org/10.2969/jmsj/03340605

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Published: 1981 Received: January 30, 1980 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) C. O. Bloom and N. D. Kazarinoff, Energy decays locally even if total energy grows algebraically with time, J. Differential Equation, 16 (1974), 352-372.
2) J. Cooper, Local decay of solutions of the wave equation in the exterior of a moving body, J. Math. Anal. Appl., 49 (1975), 130-153.
3) J. Cooper and W. A. Strauss, Energy boundedness and decay of waves reflecting off a moving obstacle, Indiana Univ. Math. J., 25 (1976), 671-690.
4) P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, New York, 1967.
5) O. A. Ladyzenskaya, On the principle of limiting amplitude, Uspehi Mat. Nauk, 12 (1957) No. 3(75), 161-164.
6) C. Morawetz, Exponential decay of solutions of the wave equation, Comm. Pure Appl. Math., 19 (1966), 439-444.
7) W. A. Strauss, Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Math., 28 (1975), 265-278.
8) H. Tamura, Local energy decays for wave equations with time-dependent coefficients, Nagoya Math. J., 71 (1978), 107-123.
9) H. Tamura, On the decay of the local energy for wave equations with a moving obstacle, Nagoya Math. J., 71 (1978), 125-147.
10) D. Thoe, On the exponential decay of solutions of the wave equation, J. Math. Anal. Appl., 16 (1966), 333-346.
11) C. H. Wilcox, Scattering theory for the d'Alembert equation in exterior domains. Lecture notes in Math., 442, Springer-Verlag, 1975.

Right : [1] C. O. Bloom and N. D. Kazarinoff, Energy decays locally even if total energy grows algebraically with time, J. Differential Equation, 16 (1974), 352-372.
[2] J. Cooper, Local decay of solutions of the wave equation in the exterior of a moving body, J. Math. Anal. Appl., 49 (1975), 130-153.
[3] J. Cooper and W. A. Strauss, Energy boundedness and decay of waves reflecting off a moving obstacle, Indiana Univ. Math. J., 25 (1976), 671-690.
[4] P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, New York, 1967.
[5] O. A. Ladyzenskaya, On the principle of limiting amplitude, Uspehi Mat. Nauk, 12 (1957) No. 3 (75), 161-164.
[6] C. Morawetz, Exponential decay of solutions of the wave equation, Comm. Pure Appl. Math., 19 (1966), 439-444.
[7] W. A. Strauss, Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Math., 28 (1975), 265-278.
[8] H. Tamura, Local energy decays for wave equations with time-dependent coefficients, Nagoya Math. J., 71 (1978), 107-123.
[9] H. Tamura, On the decay of the local energy for wave equations with a moving obstacle, Nagoya Math. J., 71 (1978), 125-147.
[10] D. Thoe, On the exponential decay of solutions of the wave equation, J. Math. Anal. Appl., 16 (1966), 333-346.
[11] C. H. Wilcox, Scattering theory for the d'Alembert equation in exterior domains. Lecture notes in Math., 442, Springer-Verlag, 1975.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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