Title: Explicit conditions for the uniqueness of solutions for parabolic degenerate problems

Authors: Adama Ouedraogo

Addresses: Université Polytechnique de Bobo-Dioulasso, Département de Mathématiques, 01 BP 1091, Bobo-Dioulasso 01, Burkina-Faso, Africa

Abstract: Our purpose is to explicit the assumptions of a technical and fundamental lemma which has been used in many works as a main tool to get the uniqueness of solutions for some nonlinear and degenerate parabolic problems. In our investigation, we hope to generalise this result in a class of Hölder convection-diffusion functions. We also complete and validate the previous works by proving that the class of functions satisfying these hypotheses is not empty.

Keywords: anisotropic diffusion; degenerate parabolic problems; entropy solution; Hölder continuous functions; isotropic diffusion.

DOI: 10.1504/IJDSDE.2016.074582

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.1, pp.75 - 86

Received: 17 Feb 2015
Accepted: 02 Aug 2015

Published online: 05 Feb 2016 *

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