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.
Paolini, M., Bellettini, G., Amato, S., The nonlinear multidomain model: a new formal asymptotic analysis, in Chambolle, A., Novaga, M., Valdinoci, E. (ed.), Geometric Partial Differential Equations proceedings, Scuola Normale Superiore di Pisa, Pisa 2013: 33- 74 [http://hdl.handle.net/10807/52287]
The nonlinear multidomain model: a new formal asymptotic analysis
Paolini, Maurizio;Bellettini, Giovanni;
2013
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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