Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems. (Q2629091)

The authors study a class of partly dissipative reaction-diffusion systems (i.e. coupled reaction-diffusion-ODE equations) with homogeneous Neumann boundary conditions. They point out a Turing-type instability which destabilizes constant steady states and induces a blow-up of nonnegative spatially heterogeneous solutions. Essentially, they prove that the lack of diffusion in one of the balance equations leads automatically to a finite-time blow-up of (nonnegative spatially heterogeneous) solutions.