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July, 2000 A semilinear elliptic equation in a thin network-shaped domain
Satoshi KOSUGI
J. Math. Soc. Japan 52(3): 673-697 (July, 2000). DOI: 10.2969/jmsj/05230673

Abstract

We consider a semilinear elliptic equation in a varying thin domain of Rn. This thin domain degenerates into a geometric graph when a certain parameter tends to zero. We determine a limit equation on the graph and we prove that a solution of the PDE converges to a solution of the limit equation. Conversely, when a solution of the limit equation is given, we construct a solution of the PDE approaching a solution of the limit equation.

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Satoshi KOSUGI. "A semilinear elliptic equation in a thin network-shaped domain." J. Math. Soc. Japan 52 (3) 673 - 697, July, 2000. https://doi.org/10.2969/jmsj/05230673

Information

Published: July, 2000
First available in Project Euclid: 10 June 2008

zbMATH: 0961.35050
MathSciNet: MR1760612
Digital Object Identifier: 10.2969/jmsj/05230673

Subjects:
Primary: 35J60

Keywords: semilinear elliptic equation , thin domain

Rights: Copyright © 2000 Mathematical Society of Japan

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Vol.52 • No. 3 • July, 2000
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