Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions: Further Results
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Acta Mathematica Sinica, English Series  2003, Vol. 19 Issue (4): 679-694    DOI: 10.1007/s10114-003-0257-3
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Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions: Further Results
E. M. E. ZAYED
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
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Abstract The asymptotic expansions of the trace of the heat kernel for small positive t, where {λv} are the eigenvalues of the negative Laplacian in Rn (n=2 or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary and a smooth outer boundary , where a finite number of piecewise smooth Robin boundary conditions on the components Γj (j=1,..., k) of and on the components Γj(j=k+1,...,m) of are considered such that and and where the coeffcients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of Θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained.
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E. M. E. ZAYED
Key wordsInverse problem   Heat kernel   Eigenvalues   Robin boundary conditions   Classical ideal gas     
Received: 2001-08-13;
Cite this article:   
E. M. E. ZAYED. Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions: Further Results[J]. Acta Mathematica Sinica, English Series, 2003, 19(4): 679-694.
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http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-003-0257-3      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2003/V19/I4/679
 
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