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Lattice model for fast diffusion equation |
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| Institution: | 1. Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110, Salvador, Brazil;2. Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110, Salvador, Brazil;1. Istituto per le Applicazioni del Calcolo, CNR, Roma, Italy;2. Dipartimento di Informatica, Università di Torino, Italy;3. Dipartimento di Elettronica, Politecnico di Torino, Italy |
| Abstract: | We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero. In order to capture this fast diffusion effect from a microscopic point of view we are led to consider a proper rescaling of a model with a typically high number of particles per site. Furthermore, we obtain some results on the convergence for the method of lines for FDE. |
| Keywords: | Fast diffusion equation Zero-range Relative entropy method |
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