Differential and Integral Equations

Mathematical analysis of a model of chemotaxis with competition terms

Akisato Kubo and J. Ignacio Tello

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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

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

First available in Project Euclid: 9 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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