Artículo
Asymptotic behaviour of the nonautonomous SIR equations with diffusion
Autor/es | Anguiano Moreno, María
Kloeden, Peter E. |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2014 |
Fecha de depósito | 2024-05-03 |
Resumen | The existence and uniqueness of positive solutions of a nonautonomous system of SIR equations with diffusion are established as well as the continuous dependence of such solutions on initial data. The proofs are facilitated ... The existence and uniqueness of positive solutions of a nonautonomous system of SIR equations with diffusion are established as well as the continuous dependence of such solutions on initial data. The proofs are facilitated by the fact that the nonlinear coefficients satisfy a global Lipschitz property due to their special structure. An explicit disease-free nonautonomous equilibrium solution is determined and its stability investigated. Uniform weak disease persistence is also shown. The main aim of the paper is to establish the existence of a nonautonomous pullback attractor is established for the nonautonomous process generated by the equations on the positive cone of an appropriate function space. For this an energy method is used to determine a pullback absorbing set and then the flattening property is verified, thus giving the required asymptotic compactness of the process. |
Agencias financiadoras | DFG grants Ministerio de Economía y Competitividad (MINECO). España Junta de Andalucía Ayuda Incentivos Actividades Científicas Junta de Andalucía Proyecto de Excelencia Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) |
Identificador del proyecto | KL 1203/7-1
MTM2011-22411 IAC11-II-10602 P07-FQM-02468 2009/FQM314 |
Ficheros | Tamaño | Formato | Ver | Descripción |
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Anguiano_Kloeden.pdf | 324.4Kb | [PDF] | Ver/ | |