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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.16041 |
| Etiquetas: |
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- The nonlocal diffusion equation with continuous kernel $K(x,y$, with $ \int_{R} K(y,x) \, d \, y = 1$ has been proposed as a model for some evolution process with diffusion, including population models. However, in general, we don't have $ \int_Ω K(y,x) \, d \, y = 1$, as expected from its interpretation as a probability density. In this note, we propose a modification of the kernel, based on the idea of `reflection' at the boundary, familiar in one dimensional problems. We show that a similar construction is possible in higher dimensions, with the new kernel satisfying the above integral equality and being also symmetric in some special cases.