Differential and Integral Equations

Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems

Grzegorz Karch, Anna Marciniak-Czochra, Kanako Suzuki, and Jacek Zienkiewicz

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Abstract

In this paper, we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only destabilizes constant steady states but also induces blow-up of nonnegative spatially heterogeneous solutions. Solutions of this problem preserve nonnegativity and uniform boundedness of the total mass. Moreover, for the corresponding system with two non-zero diffusion coefficients, all nonnegative solutions are global in time. We prove that a removal of diffusion in one of the equations leads to a finite-time blow-up of some nonnegative spatially heterogeneous solutions.

Article information

Source
Differential Integral Equations Volume 29, Number 7/8 (2016), 715-730.

Dates
First available in Project Euclid: 3 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1462298682

Mathematical Reviews number (MathSciNet)
MR3498874

Zentralblatt MATH identifier
06604492

Subjects
Primary: 35K57: Reaction-diffusion equations 35B40: Asymptotic behavior of solutions 35K50

Citation

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako; Zienkiewicz, Jacek. Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems. Differential Integral Equations 29 (2016), no. 7/8, 715--730. https://projecteuclid.org/euclid.die/1462298682.


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