Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs
Including a Solution to Hilbert’s Fifth Problem
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Elemer E. Rosinger
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Lie group algebra differential equation group action nonlinear partial differential equation partial differential equation semigroup wave equation partial differential equations
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E.E. Rosinger
Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs
Including a Solution to Hilbert’s Fifth Problem
"This book presents a novel approach to Lie group actions on ordinary and generalized functions, based on parametric representation. This allows a global definition of arbitrary nonlinear Lie group actions on functions, including generalized functions. The parametric approach also makes possible a global definition for Lie semigroup actions. It is shown that the usual Lie group symmetries of classical solutions of smooth nonlinear PDEs will remain Lie group symmetries of generalized solutions of such equations."
—MATHEMATICAL REVIEWS
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