In this paper, we report our recent results on the asymptotic analysis of a PDE model for the motility of an eukaryotic cell. We formally derive the sharp interface limit, which describes the motion of the cell membrane. In the 1D case, we rigorously justify the limit, and, using numerical simulations, observe some surprising features, such as discontinuity of interface velocities and hysteresis. We show that nontrivial traveling wave solutions appear when the key physical parameter exceeds a critical value.
Nous présentons dans cet article des résultats récents sur l'analyse asymptotique d'un modèle EDP pour la migration de cellules eucaryotes. Nous dérivons formellement l'équation limite pour l'interface, qui décrit le mouvement de la membrane cellulaire. Dans le cas unidimensionnel, nous justifions cette limite de façon rigoureuse, et nous observons numériquement quelques propriétés surprenantes, comme par exemple une discontinuité dans les vitesses à l'interface et un phénomène d'hystérésis. Nous montrons l'apparition d'ondes de propagation non triviales quand le paramètre physique clé dépasse un certain seuil.
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Leonid Berlyand 1; Mykhailo Potomkin 1; Volodymyr Rybalko 2
@article{CRMATH_2016__354_10_986_0, author = {Leonid Berlyand and Mykhailo Potomkin and Volodymyr Rybalko}, title = {Phase-field model of cell motility: {Traveling} waves and sharp interface limit}, journal = {Comptes Rendus. Math\'ematique}, pages = {986--992}, publisher = {Elsevier}, volume = {354}, number = {10}, year = {2016}, doi = {10.1016/j.crma.2016.09.001}, language = {en}, }
TY - JOUR AU - Leonid Berlyand AU - Mykhailo Potomkin AU - Volodymyr Rybalko TI - Phase-field model of cell motility: Traveling waves and sharp interface limit JO - Comptes Rendus. Mathématique PY - 2016 SP - 986 EP - 992 VL - 354 IS - 10 PB - Elsevier DO - 10.1016/j.crma.2016.09.001 LA - en ID - CRMATH_2016__354_10_986_0 ER -
%0 Journal Article %A Leonid Berlyand %A Mykhailo Potomkin %A Volodymyr Rybalko %T Phase-field model of cell motility: Traveling waves and sharp interface limit %J Comptes Rendus. Mathématique %D 2016 %P 986-992 %V 354 %N 10 %I Elsevier %R 10.1016/j.crma.2016.09.001 %G en %F CRMATH_2016__354_10_986_0
Leonid Berlyand; Mykhailo Potomkin; Volodymyr Rybalko. Phase-field model of cell motility: Traveling waves and sharp interface limit. Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 986-992. doi : 10.1016/j.crma.2016.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.09.001/
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