Non-Fickian delay reaction�diffusion equations: Theoretical and numerical study
- Autores: J.R. Branco, J.A. Ferreira, Pascal da Silva
- Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 5, 2010, págs. 531-549
- Idioma: inglés
- DOI: 10.1016/j.apnum.2010.01.003
- Texto completo no disponible (Saber más ...)
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Resumen
The Fisher's equation is established combining the Fick's law for the flux and the mass conservation law with a reaction term evaluated at the present time. If this term depends on the solution at some past time, a delay parameter is introduced and the delay Fisher's equation is obtained. Modifying the Fick's law for the flux considering a time memory term, integro�differential equations of Volterra type are established.
In this paper we study reaction�diffusion equations obtained combining the two modifications: a time memory term in the flux and a delay parameter in the reaction term. The delay integro�differential equations also known as delay Volterra integro�differential equations, are studied in the theoretical view point: stability estimates are established. Numerical methods which mimic the theoretical models are analysed. Numerical experiments illustrating the established results are also included.
