front propagation in geometric and phase field models of stratified media推荐.pdf

Front propagation in geometric and phase field models of stratified media 4 A. Cesaroni∗ C. B. Muratov† M. Novaga‡ 1 0 2 October 8, 2014 t c O 7 Abstract ] We study front propagation problems for forced mean curvature flows and their P phase field variants that take place in stratified media, i.e., heterogeneous media whose A characteristics do not vary in one direction. We consider phase change fronts in in- . h finite cylinders whose axis coincides with the symmetry axis of the medium. Using t the recently developed variational approaches, we provide a convergence result relating a m asymptotic in time front propagation in the diffuse interface case to that in the sharp interface case, for suitably balanced nonlinearities of Allen-Cahn type. The result is es- [ tablished by using arguments in the spirit of Γ-convergence, to obtain a correspondence 2 between the minimizers of an exponentially weighted Ginzburg-Landau type functional v and the minimizers of an exponentially weighted area type functional. These minimiz- 3 7 ers yield the fastest traveling waves invading a given stable equilibrium in the respective 6 models and determine the asymptotic propagation speeds for front-like initial data. We 2 further show that generically these fronts are the exponentially stable global attractors 0. for this kind of initial data and give sufficient conditions under which complete phase 1