Symmetry group analysis of weak solutions

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.