Symmetry group analysis of weak solutions

Details Symmetry group analysis of weak solutions Symmetry group analysis of weak solutions

2001-04-04

arxiv.org/abs/math/0104055v2

Proc. London Math. Soc. 84 (3), 686-710, 2002

Mathematics

Functional Analysis

25 pages, final version, to appear in Proc. London Math. Soc

Scientific paper

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

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