| 概要 |
I will discuss front propagation problems for forced mean curvature flow and their phase field variants that take place in stratified media, i.e., heterogeneous media whose characteristics do not vary in one direction. I will present a convergence result relating asymptotic in time front propagation in the di ffuse interface case to that in the sharp interface case for suitably balanced nonlinearities of Allen-Cahn type. The result is obtained using a variational approach, more precisely by establishing Gamma-convergence of an exponentially weighted Ginzburg-Landau-type functional to an exponentially weighted area-type functional, whose minimizers yield the fastest moving traveling waves in the corresponding models and determine the asymptotic propagation speeds for frontlike initial data. I will further show that generically these fronts are the exponentially stable global attractors for this kind of initial data and I will give su fficient conditions under which complete phase change occurs via the formation of the considered fronts. This work has been done in collaboration with C.B. Muratov (New Jersey Institute of Technology) and M. Novaga (University of Pisa).
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