Symmetry group analysis of weak solutions
Functional Analysis
2007-05-23 v2 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.math/0104055,
title = {Symmetry group analysis of weak solutions},
author = {N. Dapic and M. Kunzinger and S. Pilipovic},
journal= {arXiv preprint arXiv:math/0104055},
year = {2007}
}
Comments
25 pages, final version, to appear in Proc. London Math. Soc