TY - JOUR
T1 - Phase-field model of cell motility
T2 - Traveling waves and sharp interface limit
AU - Berlyand, Leonid
AU - Potomkin, Mykhailo
AU - Rybalko, Volodymyr
N1 - Publisher Copyright:
© 2016
PY - 2016/10/1
Y1 - 2016/10/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84992372709&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84992372709&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2016.09.001
DO - 10.1016/j.crma.2016.09.001
M3 - Article
AN - SCOPUS:84992372709
SN - 1631-073X
VL - 354
SP - 986
EP - 992
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 10
ER -