Author:B. V. Budaev Translated by:S. Kislyakov Original publication:
Algebra i Analiz, tom 22 (2010), nomer 6.
Journal:
St. Petersburg Math. J. 22 (2011), 877-881
MSC (2010):
Primary 81Q30
Posted:
August 18, 2011
MathSciNet review:2798765 Full-text PDF
Abstract: The possibility is discussed to improve the ray approximation up to an exact representation of a wave field by the Feynman-Kac probabilistic formula (this formula gives an exact solution of the Helmholtz equation in the form of the expectation of a certain functional on the space of Brownian random walks). Some examples illustrate an application of the solutions obtained to diffraction problems.
1.V.
M. \cyr{B}abich and V.
S. \cyr{B}uldyrev, Asimptoticheskie metody v zadachakh difraktsii
korotkikh voln. Tom l, Izdat. “Nauka”, Moscow, 1972
(Russian). Metod etalonnykh zadach. [The method of canonical problems];
With the collaboration of M. M. Popov and I. A. Molotkov. MR 0426630
(54 #14569) V.
M. Babič and V.
S. Buldyrev, Short-wavelength diffraction theory, Springer
Series on Wave Phenomena, vol. 4, Springer-Verlag, Berlin, 1991.
Asymptotic methods; Translated from the 1972 Russian original by E. F.
Kuester. MR
1245488 (94f:78004)
2.Mark
Freidlin, Functional integration and partial differential
equations, Annals of Mathematics Studies, vol. 109, Princeton
University Press, Princeton, NJ, 1985. MR 833742
(87g:60066)
V. M. Babich and V. S. Buldyrev, Asymptotic methods in diffraction problems of short-length waves. The method of canonical problems, Nauka, Moscow, 1972; English transl., Short-wavelength diffraction theory. Asymptotic methods, Springer Series on Wave Phenomena, vol. 4, Springer-Verlag, Berlin, 1991. MR 0426630 (54:14569); MR 1245488 (94f:78004)
B. V. Budaev Affiliation:
Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740
Email:
budaev@berkeley.edu
