Computation of Morse decompositions for semilinear elliptic PDEs

Authors
Smiley, MW Chun, C
Citation
Mw. Smiley et C. Chun, Computation of Morse decompositions for semilinear elliptic PDEs, NUMER M P D, 17(3), 2001, pp. 290-312
Citations number
28
Categorie Soggetti
Engineering Mathematics
Journal title
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN journal
0749159X → ACNP
Volume
17
Issue
3
Year of publication
2001
Pages
290 - 312
Database
ISI
SICI code
0749-159X(200105)17:3<290:COMDFS>2.0.ZU;2-9
Abstract
A numerical method for computing all solutions of an elliptic boundary valu e problem Au + g[u, lambda] = 0 and their Morse indices as steady-states of the parabolic problem u(t) + Au + g[u, lambda] = 0, is presented. Morse de compositions are also determined. The method uses a finite element approach that is based on the method of alternative problems. Error estimates for t he finite element approximations are verified and tramples are given. (C) 2 001 John Wiley & Sons, Inc.