The diffusive limit of the Vlasov-Fokker-Planck equation with the chemotactic sensitivity coupled to a parabolic equation

Abstract

In this paper, we study the Vlasov-Fokker-Plank (VFP) equation coupled to the parabolic equation with the inclusion of the chemotactic sensitivity of the cells. The diffusive limit of the model to the Keller-Segel model with chemotaxis is investigated. In this process, we study the global existence of solutions in W-1,W-P and use energy and entropy estimates on weighted W-1,W-p of that model with a diffusive scaling. Based on this information, we deal with a diffusive limit for the model and its solution. (C) 2019 Elsevier Inc. All rights reserved.