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arXiv · 1511.02510

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

Anna Marciniak-Czochra·Grzegorz Karch·Kanako Suzuki·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.

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Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki, Jacek Zienkiewicz. 2015-11-08. Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems. https://arxiv.org/abs/1511.02510

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