EXISTENCE AND UNIQUENESS OF SOLUTION FOR
SPECIAL NONLOCAL DIFFUSION MODEL
WITH NONLINEAR FLUX
Cesar A. Gómez1, Mauricio Bogoya2
1Department of Mathematics
Universidad Nacional de Colombia
Bogotá, COLOMBIA
2Department of Mathematics
Universidad Nacional de Colombia
Bogotá, COLOMBIA

Abstract


Abstract. Using the Banach Fixed Point Theorem, we show the existence and uniqueness of solution for the following nonlocal diffusion problem with Neumann conditions

\begin{displaymath} \begin{cases} \displaystyle u_t(x,t)=(J*u(x,t))-u(x,t) +\dis... ...=u_0(x), \,\,\,\,\,\,\,\,\,\,x\in\overline{\Omega}, \end{cases}\end{displaymath}

in which, we consider for the boundary conditions the border of a special domain $\partial\Omega\subseteq\mathbb{R^N}$, instead of the complement used previously by other authors. With this, we show the calculations are reduced in a satisfactory way and therefore, we have a new model which is a complement of a previous work where the authors use a linear flux. In this new model, the flux in the border is considered as no lineal. Finally, a comparison principle is considered.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 5
Year: 2023

DOI: 10.12732/ijam.v36i5.1

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