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| Mathematical models of a pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations will be discussed. In such models, a certain natural (autocatalysis) property of the system leads to the instability of all inhomogeneous stationary solutions. We have proved, moreover, that space inhomogeneous solutions of these models become unbounded in either finite or infinite time, even if space homogeneous solutions are bounded uniformly in time. |
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