We consider an initial boundary value problem for the heat equation in a plane two-level junction which is the union of a domain and a large number 2N of thin rods with the variable thickness of order ε= O(1/N). The thin rods are divided into two levels depending on boundary conditions given on their sides. In addition, the boundary conditions depend on some parameters , and the thin rods from each level are "-pe- riodically alternated. The asymptotic analysis of this problem for different values of the parameyers is made as ε→0. The leading terms of the asymptotic expansion for the solution are constructed, the asymptotic estimate in the Sobolev space.
Asymptotic analysis of a parabolic problem in a thick two- level junction.
DURANTE, Tiziana;
2007-01-01
Abstract
We consider an initial boundary value problem for the heat equation in a plane two-level junction which is the union of a domain and a large number 2N of thin rods with the variable thickness of order ε= O(1/N). The thin rods are divided into two levels depending on boundary conditions given on their sides. In addition, the boundary conditions depend on some parameters , and the thin rods from each level are "-pe- riodically alternated. The asymptotic analysis of this problem for different values of the parameyers is made as ε→0. The leading terms of the asymptotic expansion for the solution are constructed, the asymptotic estimate in the Sobolev space.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
