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https://hdl.handle.net/10316/11289
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. | URI: | https://hdl.handle.net/10316/11289 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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File | Description | Size | Format | |
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Non-Fickian delay reaction-diffusion equations.pdf | 1.08 MB | Adobe PDF | View/Open |
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