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Short-time asymptotics of the trace of the wave operator for a general annular drum in R-2 with Robin boundary conditions
Faculty
Not Specified
Year:
2001
Type of Publication:
Article
Pages:
493-500
Authors:
ZAYED, EME, Abdel-Halim, IH
Journal:
INDIAN JOURNAL OF PURE \& APPLIED MATHEMATICS INDIAN NAT SCI ACAD
Volume:
32
Research Area:
Mathematics
ISSN
ISI:000169593600002
Keywords :
short time asymptotics, wave operator, Laplacian in R-2, Robin boundary conditions, heat equation, kernel, wave equation, annular drum, inverse problem, eigenvalues
Abstract:
Short-time asymptotics of the trace of the wave operator <(<mu>)over cap>(t)= {[}GRAPHICS] exp(-it mu (1/2)(j)), where \{mu\}(j=1)(infinity) are the eigenvalues of the negative Laplacian in R-2, is Studied for a variety of domains, where -infinity < t < infinity and i = root -1. The dependance of <(<mu>)over cap>(t) on the connectivity of bounded drums and the Robin boundary conditions are analyzed. Particular attention is given to a general annular drum in R-2 together with the Robin boundary conditions on its boundaries.
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