Publication
Non-Fickian delay reaction-diffusion equations: theoretical and numerical study
| Summary: | 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. |
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| Main Authors: | Ferreira, J. A. |
| Other Authors: | Branco, J. R.; Silva, P. da |
| Subject: | Delay reaction-diffusion equation Integro-differential equation Retarded Volterra integro-differential equations Numerical method Stability Convergence |
| Year: | 2007 |
| Country: | Portugal |
| Document type: | preprint |
| Access type: | open access |
| Associated institution: | Universidade de Coimbra |
| Language: | English |
| Origin: | Estudo Geral - Universidade de Coimbra |
| Summary: | 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. |
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