An inverse problem for a general annular drum with positive smooth functions in the Robin boundary conditions

E. M. E. Zayed

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An inverse problem for a general annular drum with positive smooth functions in the Robin boundary conditions

Autores: E. M. E. Zayed
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 51, Fasc. 3, 2000, págs. 261-276
Idioma: inglés
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Resumen
- The asymptotic expansion of the trace of the heat kernelΘ(t)=∞j=1exp(−tλj)ast→0+has been derived for a variety of domains, where{λj}are the eigenvalues of the negative Laplace operator−∆=−2i=1(∂∂xi)2in the(x1,x2)-plane. The dependence ofΘ(t)on the connectivity of domainsand the boundary conditions is analyzed. Particular attention is given for a ge-neral annular drum inR2together with Robin boundary conditions, where thecoefficients in the boundary conditions are positive smooth functions. Someapplications of an ideal gas enclosed in the general annular drum are given.
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