Translator Disclaimer
MArch/April 2009 Concentration of solutions of a semilinear PDE with slow spatial dependence
Robert Magnus
Adv. Differential Equations 14(3/4): 341-374 (MArch/April 2009).

Abstract

The problem $-\epsilon^2\nabla\cdot(P( x)\nabla u)+F(V( x),u)=0$ is studied in the whole of ${\mathbb R}^n$, where $V(x)$ is a multidimensional potential and $P(x)$ a matrix function. Under general conditions solutions are constructed for small positive $\epsilon$ having simple concentration properties. The asymptotic form of the solution is studied as $\epsilon\to 0$ as well as its positivity.

Citation

Download Citation

Robert Magnus. "Concentration of solutions of a semilinear PDE with slow spatial dependence." Adv. Differential Equations 14 (3/4) 341 - 374, MArch/April 2009.

Information

Published: MArch/April 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1165.35018
MathSciNet: MR2493565

Subjects:
Primary: 35J60

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.14 • No. 3/4 • MArch/April 2009
Back to Top