caa a22 4500 605514984 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00205-014-0804-3 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0804-3 Front Propagation in Geometric and Phase Field Models of Stratified Media [Elektronische Daten] [Annalisa Cesaroni, Cyrill Muratov, Matteo Novaga] We study front propagation problems for forced mean curvature flows and their phase field variants that take place in stratified media, that is, heterogeneous media whose characteristics do not vary in one direction. We consider phase change fronts in infinite cylinders whose axis coincides with the symmetry axis of the medium. Using the recently developed variational approaches, we provide a convergence result relating 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 established by using arguments in the spirit of Γ-convergence, to obtain a correspondence between the minimizers of an exponentially weighted Ginzburg-Landau type functional and the minimizers of an exponentially weighted area type functional. These minimizers yield the fastest traveling waves invading a given stable equilibrium in the respective models and determine the asymptotic propagation speeds for front-like initial data. We further show that generically these fronts are the exponentially stable global attractors for this kind of initial data and give sufficient conditions under which complete phase change occurs via the formation of the considered fronts. Springer-Verlag Berlin Heidelberg, 2014 Cesaroni Annalisa Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padua, Italy aut Muratov Cyrill Department of Mathematical Sciences, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut Novaga Matteo Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 153-191 0003-9527 216:1<153 2015 216 205 https://doi.org/10.1007/s00205-014-0804-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0804-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cesaroni Annalisa Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padua, Italy aut NATIONALLICENCE 700 1- Muratov Cyrill Department of Mathematical Sciences, New Jersey Institute of Technology, 07102, Newark, NJ, USA aut NATIONALLICENCE 700 1- Novaga Matteo Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 153-191 0003-9527 216:1<153 2015 216 205