A Microscopic Model for a One Parameter Class of Fractional Laplacians with Dirichlet Boundary Conditions
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| Autores: | , , |
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| Formato: | artículo |
| Fecha de Publicación: | 2021 |
| Descripción: | We prove the hydrodynamic limit for the symmetric exclusion process with long jumps given by a mean zero probability transition rate with infinite variance and in contact with infinitely many reservoirs with density α at the left of the system and β at the right of the system. The strength of the reservoirs is ruled by κN−θ > 0. Here N is the size of the system, κ > 0 and θ ∈ R. Our results are valid for θ ≤ 0. For θ = 0, we obtain a collection of fractional reaction–diffusion equations indexed by the parameter κ and with Dirichlet boundary conditions. Their solutions also depend on κ. For θ < 0, the hydrodynamic equation corresponds to a reaction equation with Dirichlet boundary conditions. The case θ > 0 is still open. For that reason we also analyze the convergence of the unique weak solution of the equation in the case θ = 0 when we send the parameter κ to zero. Indeed, we conjecture that the limiting profile when κ → 0 is the one that we should obtain when taking small values of θ > 0 |
| País: | Repositorio UNA |
| Institución: | Universidad Nacional de Costa Rica |
| Repositorio: | Repositorio UNA |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:null:11056/21565 |
| Acceso en línea: | http://hdl.handle.net/11056/21565 |
| Palabra clave: | HYDRODYNAMIC LIMIT HEAT EQUATIONS BONDARY CONDITIONS MODELOS MATEMÁTICOS ECUACIONES DIFERENCIALES |