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Scattering of plane waves by a moving obstacle. (English) Zbl 0412.35074


MSC:

35P25 Scattering theory for PDEs
35L70 Second-order nonlinear hyperbolic equations
35L05 Wave equation
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI

References:

[1] Buchal, R.N., The approach to steady state solutions of exterior boundary value problems for the wave · Zbl 0108.28302
[2] Cooper, J., Local energy decay of solutions of the wave equation in the exterior of a moving bo · Zbl 0294.35046 · doi:10.1016/0022-247X(75)90165-1
[3] Cooper, J. & W. Strauss, Energy boundedness and decay of waves reflecting off a moving obstacle, Indiana J. Math., 25, 671–690 (1976) · Zbl 0348.35059 · doi:10.1512/iumj.1976.25.25052
[4] Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. 2, New York: Interscience 1953 · Zbl 0051.28802
[5] Fock, V., Theory of Space Time and Gravitation, New York: Macmillan (1964) · Zbl 0085.42301
[6] Friedlander, F.G., An Inverse Problem for Radiation Fields, · Zbl 0286.35050 · doi:10.1112/plms/s3-27.3.551
[7] Lax, P. & R. Phillips, Scattering Theory, New York and London: Academic Press 1967
[8] Morawetz, C., The Limiting Amplitude Principle · Zbl 0196.41202 · doi:10.1002/cpa.3160150303
[9] Morawetz, C., Exponential decay of solutions of the wave equation · Zbl 0161.08002 · doi:10.1002/cpa.3160190407
[10] Niznik, L.P., The Scattering Problem for Non-stationary Perturbations, Doklady: Soviet Math. Vol. 1, 478–481 (1960) · Zbl 0098.29802
[11] Strauss, W., Decay of solutions of hyperbolic equations with localized nonlinear terms, Symposia Mathematica VII, Inst. Naz. Alta. Mat. Rome 339–355 (1971)
[12] Wilcox, C., A generalization of the theorems of Rellich an · Zbl 0074.08102 · doi:10.1090/S0002-9939-1956-0078912-4
[13] Wilcox, C., Spherical Means and Radiation Conditions, Arch. Rational Mech. Anal., 3, 133–148 (1959) · Zbl 0087.09603 · doi:10.1007/BF00284171
[14] Wilcox, C., Scattering Theory for The d’Alembert Equation in Exterior Domains, Lecture Notes in Mathematics #442, Berlin and New York: Springer 1975 · Zbl 0299.35002
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