| Abstract: |
| We discuss systems of a single reaction-diffusion equation coupled with an ordinary differential equation. Such systems of equations are often used as models of pattern formation phenomena, which arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusion signaling factors.
We show that all continuous spatially heterogeneous stationary solutions can be unstable in most cases. Therefore, even if it is a model of pattern formation, there is no stable spatial pattern, which is very different from classical reaction-diffusion models. Moreover, we see that space inhomogeneous solutions of some reaction-diffusion-ODE systems become unbounded in either finite or infinite time, even if space homogeneous solutions are bounded uniformly in time. We would like to understand a mechanism of the growing solutions in infinite time.
These are joint works with A. Marciniak-Czochra (University of Heidelberg) and G. Karch (University of Wroclaw). |
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