Well-posedness of an evolution problem with nonlocal diffusion
| Autor: | Gonzalo Galiano |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Integrable system
Population Mathematics::Analysis of PDEs Hölder condition Monotonic function 01 natural sciences Mathematics - Analysis of PDEs FOS: Mathematics Applied mathematics 0101 mathematics education Mathematics education.field_of_study Applied Mathematics 010102 general mathematics General Engineering General Medicine Lipschitz continuity 010101 applied mathematics Computational Mathematics Range (mathematics) Kernel (statistics) Bounded variation General Economics Econometrics and Finance Analysis Analysis of PDEs (math.AP) |
| Popis: | We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Holder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics. |
| Databáze: | OpenAIRE |
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