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

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 \(Ω^n\), where \(n≥ 1\) and \(∂Ω\) is smooth. We assume that the parameters in the system are positive constants. Additionally, the initial data \((u₁₀, u₂₀, v₁₀, v₂₀)∈ L^2(Ω)× L^2(Ω) × W1,2(Ω)× W1,2(Ω)\) are non-negative. The existence of a weak solution to the problem is established using energy inequality method. For more information see https://ejde.math.txstate.edu/Volumes/2024/56/abstr.html