Approximation of a semigroup model of anomalous diffusion in a bounded set
Stephen Thompson Thomas I. Seidman
Evolution Equations & Control Theory 2013, 2(1): 173-192 doi: 10.3934/eect.2013.2.173
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.
keywords: Trotter-Kato theorem mathematical epidemiology. anomalous diffusion regional fractional Laplacian Reflected stable process operator semigroup

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