Existence of weak solutions to the Keller–Segel chemotaxis system with additional cross-diffusion

Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Gurusamy Arumugam, André H. Erhardt, Indurekha Eswaramoorthy, Balachandran KrishnanAbstractIn this paper, we consider the Keller–Segel chemotaxis system with additional cross-diffusion term in the second equation. This system is consisting of a fully nonlinear reaction–diffusion equations with additional cross-diffusion. We establish the existence of weak solutions to the considered system by using Schauder’s fixed point theorem, a priori energy estimates and the compactness results.

Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research