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

2008/09/23 by Jorge Aragona, J. Aragona, Antônio Ronaldo Gomes Garcia +6
Arts and Humanities · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Philosophy and History of Science #Probability and Statistical Research #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.0809.3837

arxiv created 2008/09/23 · openalex publication_date 2008/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citebf Brézis and Friedman prove that certain nonlinear parabolic equations, with the δ-measure as initial data, have no solution. However in \citecl Colombeau and Langlais prove that these equations have a unique solution even if the δ-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 \citeA.

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