Open AccessQualitative and quantitative analysis for a nonlocal and nonlinear reaction-diffusion problem with in-homogeneous Neumann boundary conditions
Author(s) -
Costică Moroşanu,
Bianca Satco
Publication year - 2023
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022042
Subject(s) - uniqueness , mathematics , neumann boundary condition , mathematical proof , reaction–diffusion system , fixed point theorem , class (philosophy) , boundary value problem , homogeneous , nonlinear system , scheme (mathematics) , mathematical analysis , boundary (topology) , von neumann architecture , pure mathematics , computer science , physics , combinatorics , geometry , quantum mechanics , artificial intelligence
The main goal of this paper is to introduce and analyze a new nonlocal reaction-diffusion model with in-homogeneous Neumann boundary conditions. We prove the existence and uniqueness of a solution in the class \begin{document}$ C((0, T], L^\infty(\Omega)) $\end{document} and the dependence on the data. Proofs are based on the Banach fixed-point theorem. Our results extend the results already proven by other authors. A numerical approximating scheme and a series of numerical experiments are also presented in order to illustrate the effectiveness of the theoretical result. The overall scheme is explicit in time and does not need iterative steps; therefore it is fast.