Premium
Symmetry Group Analysis of Weak Solutions
Author(s) -
Đapić N.,
Kunzinger M.,
Pilipović S.
Publication year - 2002
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013436
Subject(s) - mathematics , infinitesimal , symmetry (geometry) , factorization , term (time) , weak solution , symmetry group , lie group , work (physics) , pure mathematics , mathematical analysis , mechanical engineering , physics , geometry , algorithm , quantum mechanics , engineering
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.