INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

Abstract

Abstract:

This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =P1 μ=1 exp(−tμ), where {μ}1 μ=1 are the eigenvalues of the negative Laplacian −n = −Pn p=1( @ @xp )2 in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum which is surrounded by simply connected bounded domainsi with smooth boundaries @ i(i = 1, · · · ,m) where the Dirichlet, Neumann and Robin
boundary conditions on @i(i = 1, · · · ,m) are considered. Some geometrical properties of are determined. The thermodynamic quantities for an ideal gas enclosed in are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container , although it can feel some geometrical properties of it.

Key words: Inverse problem, heat kernel, eigenvalues, an ideal gas, multi-connected bounded domain

CLC Number:

35K99

E.M.E.Zayed. INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS[J].Acta mathematica scientia,Series B, 2003, 23(1): 104-116.

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