We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.
Amato, S., Bellettini, G., Paolini, M. (2013). The nonlinear multidomain model: a new formal asymptotic analysis. In Geometric Partial DifferentialEquations, Proceedings (pp.33-72) [10.1007/978-88-7642-473-1_2].
The nonlinear multidomain model: a new formal asymptotic analysis
BELLETTINI, GIOVANNI;
2013-01-01
Abstract
We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.
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https://hdl.handle.net/11365/1017528