New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations

Svetlin G. Georgiev; Khaled Zennir

doi:10.4067/S0719-06462018000200023

Authors

Svetlin G. Georgiev Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sorbonne University, Paris, France.
Khaled Zennir Department of Mathematics, College of Sciences and Arts, Al-Ras. Qassim University, Kingdom Of Saudi Arabia.

DOI:

https://doi.org/10.4067/S0719-06462018000200023

Keywords:

parabolic equation, existence, differentiability with respect to the initial data

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.