Homogenization of a parabolic signorini boundary value problem in a thick plane junction

被引：0
作者：
T. A. Mel’nyk
Iu. A. Nakvasiuk
机构：
[1] National Taras Shevchenko University of Kyiv,
来源：
Journal of Mathematical Sciences | 2012年 / 181卷 / 5期
关键词：
Weak Solution; Variational Inequality; Parabolic Problem; Integral Inequality; Unique Weak Solution;
D O I：
10.1007/s10958-012-0708-4
中图分类号：
学科分类号：
摘要：
We consider a parabolic Signorini boundary value problem in a thick plane junction Ωε which is the union of a domain Ω0 and a large number of ε−periodically situated thin rods. The Signorini conditions are given on the vertical sides of the thin rods. The asymptotic analysis of this problem is done as ε → 0, i.e., when the number of the thin rods infinitely increases and their thickness tends to zero. With the help of the integral identity method we prove a convergence theorem and show that the Signorini conditions are transformed (as ε → 0) in differential inequalities in the region that is filled up by the thin rods in the limit passage. Bibliography: 31 titles. Illustrations: 1 figure.
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页码：613 / 631
页数：18
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