Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 56, pp. 1-16.

Title: Existence of global weak solution to tumor chemotaxis competition systems with loop and signal dependent sensitivity

Authors: Shanmugasundaram Gnanasekaran (Easwari Engineeering College, Chennai, TN, India)
         Nagarajan Nithyadevi (Easwari Engineeering College, Chennai, TN, India)

Abstract: 
This article examines the weak solution of a fully parabolic 
chemotaxis-competition system with loop and signal-dependent sensitivity. 
The system is subject to homogeneous Neumann boundary conditions within 
an open, bounded domain $\Omega\subset\mathbb{R}^n$, where $n\geq 1$ and 
$\partial\Omega$ is smooth. We assume that the parameters in the system 
are positive constants. Additionally, the initial data 
$(u_{10}, u_{20}, v_{10}, v_{20})\in L^2(\Omega)\times L^2(\Omega)
\times W^{1,2}(\Omega)\times W^{1,2}(\Omega)$ are non-negative. 
The existence of a weak solution to the problem is established using 
energy inequality method.

Submitted April 29, 2024. Published September 27, 2024.
Math Subject Classifications: 35A01, 35D30, 92C17, 35Q92.
Key Words: Chemotaxis system; two species and two stimuli; weak solution; Lotka-Volterra competition.