Differential and Integral Equations

Mathematical analysis of a model of chemotaxis with competition terms

Akisato Kubo and J. Ignacio Tello

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Abstract

We consider a competitive system of differential equations describing the behavior of two biological species ``$u$" and ``$v$". The system is weakly coupled and one of the species has the capacity to diffuse and moves toward the higher concentration of the second species following its gradient, the density function satisfies a second order parabolic equation with chemotactic terms. The second species does not have motility capacity and satisfies an ordinary differential equation. We prove that the solutions are uniformly bounded and exist globally in time. The asymptotic behavior of solutions is also studied for a range of parameters and initial data. If the chemotaxis coefficient $\chi$ is small enough the quadratic terms drive the solutions to the constant steady state.

Article information

Source
Differential Integral Equations Volume 29, Number 5/6 (2016), 441-454.

Dates
First available in Project Euclid: 9 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1457536886

Mathematical Reviews number (MathSciNet)
MR3471968

Zentralblatt MATH identifier
06562184

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations 92D40: Ecology

Citation

Kubo, Akisato; Tello, J. Ignacio. Mathematical analysis of a model of chemotaxis with competition terms. Differential Integral Equations 29 (2016), no. 5/6, 441--454. https://projecteuclid.org/euclid.die/1457536886.


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