Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-24T09:18:27.467Z Has data issue: false hasContentIssue false
  • English
  • Français

On the decay of the local energy for wave equations with a moving obstacle

Published online by Cambridge University Press:  22 January 2016

Hideo Tamura
Hideo Tamura*
Affiliation:
Department of Engineering Mathematics Faculty of Engineering, Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently the decay of the local energy for wave equations with a moving obstacle has been studied by Cooper [1] and Cooper and Strauss [2] etc. In their works it has been assumed that the obstacle is uniformly bounded in time t and that the origin is contained in for all t > 0 and is star-shaped with respect to the origin. (The second condition has been assumed implicitly in [2] (see Assumption (B), [2]).)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 71 , November 1978 , pp. 125 - 147
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

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] Cooper, J. and Strauss, W. A., Energy boundedness and decay of waves reflecting off a moving obstacle, India. Univ. Math. J., 25 (1976), 671–690.CrossRefGoogle Scholar
[3] Inoue, A., dans un domaine non-cylindrique, J. Math. Anal. Appl., 46 (1973), 777–819.Google Scholar
[4] Lax, P. and Phillips, , 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), 439–444.Google Scholar
[6] Tamura, H., Local energy decays for wave equations with time-dependent coefficients, Nagoya Math. J., 71 (1978), 107–123.CrossRefGoogle Scholar
[7] 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.Google Scholar