Soluciones viscosas ecuación parabólica no lineal.

Abstract

We present a parabolic problem, in which a non-local operator called Caputo's fractional derivative is involved. We give a previous context for the definitions that are usual in this subject. We conceptualize the definitions of viscous solutions. We present and prove results required to facilitate the proof of a theorem that assures existence of discontinuous solutions and another that will help us with uniqueness and continuity. The theorems are called Perron's method and comparison principle respectively, and finally thanks to the previous we obtain a result that assures existence and uniqueness of solutions for our problem.