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Li, Dongfang; Tong, Chao; Wen, Jinming

Stability of exact and discrete energy for non-Fickian reaction-diffusion equations with a variable delay. (English) Zbl 1474.35621

Abstr. Appl. Anal. 2014, Article ID 840573, 9 p. (2014).
Summary: This paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. Then, we prove that the proposed numerical methods are sufficient to preserve energy stability of the continuous problems. We end the paper with some numerical experiments on a biological model to confirm the theoretical results.

Cited in 4 Documents

MSC:

35R10 Partial functional-differential equations
35K57 Reaction-diffusion equations
45K05 Integro-partial differential equations
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References:

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