Nonlocal complement value problem for a global in time parabolic equation
Abstract
The overreaching goal of this paper is to investigate the existence and uniqueness of weak solution of a semilinear parabolic equation with double nonlocality in space and in time variables that naturally arises while modeling a biological nano-sensor in the chaotic dynamics of a polymer chain. In fact, the problem under consideration involves a symmetric integrodifferential operator of L\'{e}vy type and a term called the interaction potential, that depends on the time-integral of the solution over the entire interval of solving the problem. Owing to the Galerkin approximation, the existence and uniqueness of a weak solution of the nonlocal complement value problem is proven for small time under fair conditions on the interaction potential.
Cite
@article{arxiv.2102.07278,
title = {Nonlocal complement value problem for a global in time parabolic equation},
author = {Jean-Daniel Djida and Guy F. Foghem Gounoue and Yannick Kouakep Tchaptchie},
journal= {arXiv preprint arXiv:2102.07278},
year = {2022}
}
Comments
To appear in J Elliptic Parabol Equ (2022)