Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki, Jacek Zienkiewicz
Published 2015-11-08Version 1
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.
Qualitative properties and classification of nonnegative solutions to $-Δu=f(u)$ in unbounded domains when $f(0)<0$
Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace
Monotonicity and symmetry of nonnegative solutions to $ -Δu=f(u) $ in half-planes and strips
![QR code for arXiv:1511.02510 [math.AP]](http://oss.arxitics.com/images/favicon.svg)