Abstract
AbstractThe 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 Lévy 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.
Funder
Deutsche Forschungsgemeinschaft
Deutscher Akademischer Austauschdienst
Ministère de l’Enseignement Supèrieur, Republique du Cameroun
Technische Universität Dresden
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Numerical Analysis,Analysis
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