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

• Published in: Electronic journal of differential equations Vol. 2024; no. 1-??; pp. 56 - 16
• Main Authors: Gnanasekaran, Shanmugasundaram, Nithyadevi, Nagarajan
• Format: Journal Article
• Language: English
• Published: Texas State University 27.09.2024
• Subjects: chemotaxis system; lotka-volterra competition; two species and two stimuli; weak solution
• ISSN: 1072-6691; 1072-6691
• DOI: 10.58997/ejde.2024.56

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.   For more information see https://ejde.math.txstate.edu/Volumes/2024/56/abstr.html