Semilinear elliptic equations on thin network-shaped domains with variable thickness

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:183

Article

Kosugi, S

关键词: semilinear elliptic equations;    thin domains;    geometric graphs;    asymptotic behavior;   

DOI  :  10.1006/jdeq.2001.4119

来源: Elsevier

【 摘 要 】

We study semilinear elliptic equations in a thin domain which is shaped like a network and degenerate into a geometric graph when a certain parameter tends to zero. It is shown by using a comparison technique that a solution of the equation in the network-shaped domain approaches a solution of an associated limit equation on the graph. Conversely, when the limit equation on the graph has a solution, we prove the existence of a solution of the PDE in the network-shaped domain which converges to the solution of the limit equation. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free