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2000 On a nonlocal diffusion equation with discontinuous reaction
Danielle Hilhorst, José-Francisco Rodrigues
Adv. Differential Equations 5(4-6): 657-680 (2000). DOI: 10.57262/ade/1356651343


We consider the asymptotic derivation of a parabolic equation with nonlocal diffusivity and with a semi-linear nonlocal term that may also be discontinuous. From a reaction-diffusion system where the diffusivity of the second equation is arbitrarily large, using only energy estimates, we obtain a shadow system as an intermediate step for the limit equation. In particular, we obtain the existence of weak solutions and we give a rigorous derivation of a class of diffusion equations that have been used in the literature to model threshold phenomena, for instance, in porous-medium combustion or in localized patterns of excitable media.


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Danielle Hilhorst. José-Francisco Rodrigues. "On a nonlocal diffusion equation with discontinuous reaction." Adv. Differential Equations 5 (4-6) 657 - 680, 2000.


Published: 2000
First available in Project Euclid: 27 December 2012

zbMATH: 0990.35058
MathSciNet: MR1750114
Digital Object Identifier: 10.57262/ade/1356651343

Primary: 35R35
Secondary: 35K50 , 35K57

Rights: Copyright © 2000 Khayyam Publishing, Inc.


Vol.5 • No. 4-6 • 2000
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