Department of Mathematics
Easwari Engineeering College
Chennai, TN 600089, India
email: dr.sakar.mat@gmail.com
Department of Applied Mathematics
Bharathiar University
Coimbatore, TN 641046, India
email: nithyadevin@buc.edu.in
Shanmugasundaram Gnanasekaran, Nagarajan Nithyadevi
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.
DOI: 10.58997/ejde.2024.56
Show me the PDF file (375 KB), TEX file for this article.
|
Shanmugasundaram Gnanasekaran Department of Mathematics Easwari Engineeering College Chennai, TN 600089, India email: dr.sakar.mat@gmail.com |
|---|---|
|
Nagarajan Nithyadevi Department of Applied Mathematics Bharathiar University Coimbatore, TN 641046, India email: nithyadevin@buc.edu.in |
Return to the EJDE web page