Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 301
REGULARITY FOR THE FRACTIONAL HEAT EQUATION AND APPLICATION
Somia Atmani
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 30, 2022
March 03, 2260
April 15, 2260

Abstract: The aim of our work is to study the nonlocal version of the Kardar-Parisi-Zhang equation with fractional gradient. More precisely, we consider the nonlocal problem Where Ω is a bounded domain in ℝN with N>2s, q≥1 and f, u0 are nonnegative measurable functions. To prove the existence result for the problem (P), we need to analyse deeply the question of fractional regularity to the corresponding heat fractional equation with Dirichlet condition. The main tool that we used for this purpose, is a new estimate on the heat kernel noted by P(x,y,t). The results of the present ...