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Approximation of a semigroup model of anomalous diffusion in a bounded set

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  • The convergence is established for a sequence of operator semigroups, where the limiting object is the transition semigroup for a reflected stable processes. For semilinear equations involving the generators of these transition semigroups, an approximation method is developed as well. This makes it possible to derive an a priori bound for solutions to these equations, and therefore prove global existence of solutions. An application to epidemiology is also given.
    Mathematics Subject Classification: Primary: 47D06, 60J35; Secondary: 60J75, 45L05, 58D25, 35K57, 92D30.

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