Advances in Differential Equations
- Adv. Differential Equations
- Volume 5, Number 4-6 (2000), 657-680.
On a nonlocal diffusion equation with discontinuous reaction
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.
Adv. Differential Equations Volume 5, Number 4-6 (2000), 657-680.
First available in Project Euclid: 27 December 2012
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Hilhorst, Danielle; Rodrigues, José-Francisco. On a nonlocal diffusion equation with discontinuous reaction. Adv. Differential Equations 5 (2000), no. 4-6, 657--680. https://projecteuclid.org/euclid.ade/1356651343.