Abstract
We study a singularly perturbed reaction-diffusion equation with a small
parameter $\epsilon>0$.
This problem is viewed as an approximation of the evolution
of an interface by its mean curvature with a forcing term.
We derive a quasi-optimal error estimate of order
$\O(\epsilon^2|\log\epsilon|^2)$ for the interfaces, which is valid before the onset
of singularities, by constructing suitable sub and super solutions.
The proof relies on the behaviour at infinity of functions appearing in
the truncated asymptotic expansion, and by using a modified distance
function combined with a vertical shift.
Lingua originale | English |
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pagine (da-a) | 735-752 |
Numero di pagine | 18 |
Rivista | Differential and Integral Equations |
Stato di pubblicazione | Pubblicato - 1995 |
Keywords
- Allen-Cahn equation
- mean curvature flow