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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:91933 |
| Date | 11 June 2024 |
| Creators | Djida, Jean‑Daniel, Foghem Gounoue, Guy Fabrice, Tchaptchié, Yannick Kouakep |
| Publisher | Springer International Publishing |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 2296-9039, 10.1007/s41808-022-00175-8 |
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