We prove the existence of self-similar solutions for a heat equation with a signum type source term function of the unknown itself. We prove that surprisingly a negative source term can give rise to a solution having a region of positivity thus also proving non-uniqueness for the problem
Self-Similar Solutions for the Heat Equation with a Signum-Type Source Term / Roberto Gianni, A.F.. - In: QUARTERLY OF APPLIED MATHEMATICS. - ISSN 0033-569X. - ELETTRONICO. - (In corso di stampa), pp. 0-0.
Self-Similar Solutions for the Heat Equation with a Signum-Type Source Term
Roberto Gianni;Angiolo Farina;Fabio Rosso
In corso di stampa
Abstract
We prove the existence of self-similar solutions for a heat equation with a signum type source term function of the unknown itself. We prove that surprisingly a negative source term can give rise to a solution having a region of positivity thus also proving non-uniqueness for the problem
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