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Title: Non-Fickian delay reaction-diffusion equations: theoretical and numerical study
Authors: Ferreira, J. A. 
Branco, J. R. 
Silva, P. da 
Keywords: Delay reaction-diffusion equation; Integro-differential equation; Retarded Volterra integro-differential equations; Numerical method; Stability; Convergence
Issue Date: 2007
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 07-29 (2007)
Abstract: The Fisher’s equation is established combining the Fick’s law for the flux and the mass conservation law. Assuming that the reaction 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 temporal memory term, integro-differential equations of Volterra type were introduced in the literature. In these paper we study reaction-diffusion equations obtained combining the two modifications: a temporal memory term in the flux and a delay in the reaction term. The delay integro-differential equations, also known as delay Volterra integrodifferential equations, are studied in the theoretical view point: stability estimates are established. Numerical methods which mimic the theoretical models are studied. Numerical experiments illustrating the established results are also included.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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