Generalized Solutions of a Nonlinear Parabolic Equation with Generalized Functions as Initial Data

Details Generalized Solutions of a Nonlinear Parabolic Equation with Generalized Functions as Initial Data Generalized Solutions of a Nonlinear Parabolic Equation with Generalized Functions as Initial Data

2008-09-23

arxiv.org/abs/0809.3837v1

Mathematics

Analysis of PDEs

Scientific paper

In \cite{bf} Br\'ezis and Friedman prove that certain nonlinear parabolic equations, with the $\delta$-measure as initial data, have no solution. However in \cite{cl} Colombeau and Langlais prove that these equations have a unique solution even if the $\delta$-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais their result proving that we may take any generalized function as the initial data. Our approach relies on resent algebraic and topological developments of the theory of Colombeau generalized functions and results from \cite{A}.

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