New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations
Author
Georgiev, Svetlin G.
Zennir, Khaled
Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/204810.4067/S0719-06462018000200023
Abstract
In this article, we consider a class of nonlinear parabolic equations. We use an integral representation combined with a sort of fixed point theorem to prove the existence of classical solutions for the initial value problem (1.1), (1.2). We also obtain a result on continuous dependence on the initial data. We propose a new approach for investigation for existence of classical solutions of some classes nonlinear parabolic equations.