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SYMMETRY GROUP ANALYSIS OF WEAK SOLUTIONS

Published online by Cambridge University Press:  29 April 2002

N. ĐAPIĆ ,
M. KUNZINGER  and
S. PILIPOVIĆ
N. ĐAPIĆ
Affiliation:
Institute of Mathematics, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Yugoslavia. nenad@unsim.ns.ac.yu, pilipovic@unsim.ns.ac.yu
M. KUNZINGER
Affiliation:
Institut für Mathematik, Universität Wien, Strudlhofg. 4, A-1090 Vienna, Austria. Michael.Kunzinger@univie.ac.at
S. PILIPOVIĆ
Affiliation:
Institute of Mathematics, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Yugoslavia. nenad@unsim.ns.ac.yu, pilipovic@unsim.ns.ac.yu
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Abstract

Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and non-linear) partial differential equations, where the term `weak solution' comprises the following settings: distributional solutions; solutions in generalized function algebras; solutions in the sense of association (corresponding to a number of weak or integral solution concepts in classical analysis). Factorization properties and infinitesimal criteria that allow the treatment of all three settings simultaneously are developed, thereby unifying and extending previous work in this area.

2000 Mathematical Subject Classification: 46F30, 22E70, 35Dxx, 35A30.

Keywords

algebras of generalized functionsLie symmetries of differential equationsgroup analysisColombeau algebras
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 84 , Issue 3 , May 2002 , pp. 686 - 710
Copyright
2002 London Mathematical Society

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