Global existence and stability in a class of chemotaxis systems with lethal interactions, nonlinear diffusion and production

2025/10/17 by S. Gnanasekaran, Shanmugasundaram, Gnanasekaran, Jitraj Saha +1
Engineering · Mathematics · Medicine · #35A01 #35A09 #35B40 #35Q92 #37N25. 92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2510.15276

openalex publication_date 2025/10/17 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28

Abstract

This paper investigates a class of chemotaxis systems modeling lethal interactions in a smooth, bounded domain Ω⊂ ℝⁿ with homogeneous Neumann boundary conditions. We examine two distinct cases: (i) a fully parabolic system where both equations exhibit parabolic dynamics, and (ii) a parabolic-elliptic system featuring a parabolic first equation coupled with an elliptic second equation. Under appropriate parameter constraints, we establish the existence of unique globally bounded classical solutions for arbitrary spatial dimensions n ≥ 1. Additionally, we employ carefully constructed Lyapunov functionals to analyze the long-term behavior of solutions, obtaining rigorous asymptotic stability results.

Citations

• Global boundedness and asymptotic stability of the Keller-Segel system with logistic-type source in the whole space
• Blow-up prevention by sub-logistic sources in 2d Keller-Segel system
• Boundedness for a fully parabolic Keller-Segel model with sublinear\n segregation and superlinear aggregation
• Solvability of a Keller-Segel system with signal-dependent sensitivity\n and essentially sublinear production
• Boundedness and stabilization in a three-dimensional two-species chemotaxis-Navier--Stokes system with competitive kinetics
• Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
• Model for chemotaxis
• A user’s guide to PDE models for chemotaxis

Related

• On the global existence solution for a chemotaxis model
• Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
• Global solutions for a hyperbolic-parabolic system of chemotaxis
• The simultaneous effect of chemotaxis and alarm-taxis on the global existence and stability of a predator-prey system
• Locally bounded global solutions to a chemotaxis consumption model with\n singular sensitivity and nonlinear diffusion