Advances in Differential Equations

On a nonlocal diffusion equation with discontinuous reaction

Danielle Hilhorst and José-Francisco Rodrigues

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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.

Article information

Adv. Differential Equations, Volume 5, Number 4-6 (2000), 657-680.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 35K50 35K57: Reaction-diffusion equations


Hilhorst, Danielle; Rodrigues, José-Francisco. On a nonlocal diffusion equation with discontinuous reaction. Adv. Differential Equations 5 (2000), no. 4-6, 657--680.

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