Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
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URI: http://hdl.handle.net/10835/15781
DOI: https://doi.org/10.1007/s00033-016-0649-8
DOI: https://doi.org/10.1007/s00033-016-0649-8
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2016-04-19Resumen
In this paper, we show that smooth solutions to the Dirichlet problem for the parabolic equation can be approximated uniformly by solutions of nonlocal problems for an appropriate rescaled kernel.
In this way, we show that the usual local evolution problems with spatial dependence can be approximated by nonlocal ones. In the case of an equation in divergence form, we can obtain an approximation with symmetric kernels.