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.
Grzegorz Karch. Anna Marciniak-Czochra. Kanako Suzuki. Jacek Zienkiewicz. "Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems." Differential Integral Equations 29 (7/8) 715 - 730, July/August 2016. https://doi.org/10.57262/die/1462298682