<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we provide a method to prove the existence of weak solutions for a type of non-autonomous nonlocal reaction-diffusion equations. Due to the presence of the nonlocal operator in the diffusion term, we cannot apply the Monotonicity Method directly. To use it, we build an auxiliary problem with linear diffusion and later, through iterations and compactness arguments, we show the existence of solutions for the nonlocal problem.</p></abstract>

In this paper we provide a method to prove the existence of weak solutions for a type of non-autonomous nonlocal reaction-diffusion equations. Due to the presence of the nonlocal operator in the diffusion term, we cannot apply the Monotonicity Method directly. To use it, we build an auxiliary problem with linear diffusion and later, through iterations and compactness arguments, we show the existence of solutions for the nonlocal problem.

An iterative method for non-autonomous nonlocal reaction-diffusion equations

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"An iterative method for non-autonomous nonlocal reaction-diffusion equations"}

In this paper we provide a method to prove the existence of weak solutions for a type of non-autonomous nonlocal reaction-diffusion equations. Due to the...

An iterative method for non-autonomous nonlocal reaction-diffusion equations

Published Online: Feb 23, 2017

Page range: 73 - 82

Received: Nov 10, 2016

Accepted: Feb 23, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00006

Keywords
Nonlocal diffusion, Non-autonomous reaction-diffusion equations, monotone, iterative and compactness arguments

© 2017 Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An iterative method for non-autonomous nonlocal reaction-diffusion equations

Published Online: Feb 23, 2017

Page range: 73 - 82

Received: Nov 10, 2016

Accepted: Feb 23, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00006

KeywordsNonlocal diffusion, Non-autonomous reaction-diffusion equations, monotone, iterative and compactness arguments

© 2017 Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Nonlocal diffusion, Non-autonomous reaction-diffusion equations, monotone, iterative and compactness arguments