On the Hamilton-Jacobi equation in the framework of generalized functions |
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Authors: | Roseli Fernandez |
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Affiliation: | Departamento de Matemática, Instituto de Matemática e Estatística da Universidade de São Paulo, Caixa Postal 66281, CEP 05314-970, São Paulo, Brazil |
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Abstract: | In this work we study, in the framework of Colombeau?s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. |
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Keywords: | Generalized functions Method of characteristics Hamilton-Jacobi equation |
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