SYMMETRY GROUP ANALYSIS OF WEAK SOLUTIONS
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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.
- University of Vienna Austria
- University of Novi Sad Serbia
1010 Mathematics, Lie groups, 1010 Mathematik, Existence of generalized solutions of PDE, Functional Analysis (math.FA), Mathematics - Functional Analysis, 46F30, 22E70, 35Dxx, 35A30, Mathematics - Analysis of PDEs, Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.), FOS: Mathematics, Applications of functional analysis to differential and integral equations, conservation laws, symmetry groups, distributional solutions, Geometric theory, characteristics, transformations in context of PDEs, Analysis of PDEs (math.AP)
1010 Mathematics, Lie groups, 1010 Mathematik, Existence of generalized solutions of PDE, Functional Analysis (math.FA), Mathematics - Functional Analysis, 46F30, 22E70, 35Dxx, 35A30, Mathematics - Analysis of PDEs, Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.), FOS: Mathematics, Applications of functional analysis to differential and integral equations, conservation laws, symmetry groups, distributional solutions, Geometric theory, characteristics, transformations in context of PDEs, Analysis of PDEs (math.AP)
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