We consider a perturbed initial/boundary-value problem for the heat equation in a thick multi-structure Omega epsilon which is the union of a domain Omega(0) and a large number N of epsilon-periodically situated thin rings with variable thickness of order epsilon = O(N-1). The following boundary condition partial derivative(v)u epsilon + epsilon(alpha)k(0)u(epsilon) = epsilon(beta)g(epsilon) is given on the lateral boundaries of the thin rings; here the parameters alpha and beta are greater than or equal 1. The asymptotic analysis of this problem for di ff erent values of the parameters ff and fi is made as epsilon -> 0. The leading terms of the asymptotic expansion for the solution are constructed, the corresponding estimates in the Sobolev space L2(0, T; H1(Omega epsilon)) are obtained and the convergence theorem is proved with minimal conditions for the righthand sides.

Asymptotic analysis of a perturbed parabolic problem in a thick junction of type 3:2:2

D'APICE, Ciro;
2007-01-01

Abstract

We consider a perturbed initial/boundary-value problem for the heat equation in a thick multi-structure Omega epsilon which is the union of a domain Omega(0) and a large number N of epsilon-periodically situated thin rings with variable thickness of order epsilon = O(N-1). The following boundary condition partial derivative(v)u epsilon + epsilon(alpha)k(0)u(epsilon) = epsilon(beta)g(epsilon) is given on the lateral boundaries of the thin rings; here the parameters alpha and beta are greater than or equal 1. The asymptotic analysis of this problem for di ff erent values of the parameters ff and fi is made as epsilon -> 0. The leading terms of the asymptotic expansion for the solution are constructed, the corresponding estimates in the Sobolev space L2(0, T; H1(Omega epsilon)) are obtained and the convergence theorem is proved with minimal conditions for the righthand sides.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1846106
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