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Artículo
Nonlinear nonlocal reaction-diffusion problem with local reaction
Autor/es | Rodríguez Bernal, Aníbal
Sastre Gómez, Silvia |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2022-04-04 |
Fecha de depósito | 2023-03-03 |
Publicado en |
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Resumen | In this paper we analyse the asymptotic behaviour of some nonlocal
diffusion problems with local reaction term in general metric measure
spaces. We find certain classes of nonlinear terms, including logistic type terms,
for ... In this paper we analyse the asymptotic behaviour of some nonlocal diffusion problems with local reaction term in general metric measure spaces. We find certain classes of nonlinear terms, including logistic type terms, for which solutions are globally defined with initial data in Lebesgue spaces. We prove solutions satisfy maximum and comparison principles and give sign conditions to ensure global asymptotic bounds for large times. We also prove that these problems possess extremal ordered equilibria and solutions, asymptotically, enter in between these equilibria. Finally we give conditions for a unique positive stationary solution that is globally asymptotically stable for nonnegative initial data. A detailed analysis is performed for logistic type nonlinearities. As the model we consider here lack of smoothing effect, important focus is payed along the whole paper on differences in the results with respect to problems with local diffusion, like the Laplacian operator. |
Cita | Rodríguez Bernal, A. y Sastre Gómez, S. (2022). Nonlinear nonlocal reaction-diffusion problem with local reaction. Discrete and Continuous Dynamical Systems, 42 (4), 1731-1765. https://doi.org/10.3934/dcds.2021170. |
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