Abstract

We develop growth rates ford-dimensional domains in bistable reaction-diffusion systems. The growth of the domain is restrained by an inhibitory nonlocal interaction and leads to stable stationary inhomogeneous states as known from many applications in nonequilibrium systems. The mathematical analysis is quite similar to problems of Ostwald ripening in van-der-Waals gases though the physical mechanism is different. We show that the nonlocal interaction leads to a competition between several domains. Finally our approach is applied to optical bistability, thermokinetic systems and to nonlinear semiconductors.

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