Nonlocal complement value problem for a global in time parabolic equation

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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 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.

Details

OriginalspracheEnglisch
Seiten (von - bis)767-789
Seitenumfang23
FachzeitschriftJournal of Elliptic and Parabolic Equations
Jahrgang8
Ausgabenummer2
PublikationsstatusVeröffentlicht - Dez. 2022
Peer-Review-StatusJa

Schlagworte

Schlagwörter

  • Lévy operators, Nonlocal operators, Parabolic equations: IVP, Weak solutions