Sharp interface limit in a phase field model of cell motility

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider a phase field model of cell motility introduced in [40] which consists of two coupled parabolic PDEs. We study the asymptotic be- havior of solutions in the limit of a small parameter related to the width of the interface (sharp interface limit). We formally derive an equation of motion of the interface, which is mean curvature motion with an additional nonlin- ear term. In a 1D model parabolic problem we rigorously justify the sharp interface limit. To this end, a special representation of solutions is introduced, which reduces analysis of the system to a single nonlinear PDE that describes the interface velocity. Further stability analysis reveals a qualitative change in the behavior of the system for small and large values of the coupling parame- ter. Using numerical simulations we also show discontinuities of the interface velocity and hysteresis. Also, in the 1D case we establish nontrivial traveling waves when the coupling parameter is large enough.

Original languageEnglish (US)
Pages (from-to)551-590
Number of pages40
JournalNetworks and Heterogeneous Media
Volume12
Issue number4
DOIs
StatePublished - Dec 1 2017

Fingerprint

Cell Motility
Phase Field Model
Interfaces (computer)
Equations of motion
Hysteresis
Computer simulation
Parabolic PDEs
Nonlinear PDE
Parabolic Problems
Mean Curvature
Small Parameter
Traveling Wave
Justify
Stability Analysis
Discontinuity
Equations of Motion
Numerical Simulation
Motion
Term

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

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abstract = "We consider a phase field model of cell motility introduced in [40] which consists of two coupled parabolic PDEs. We study the asymptotic be- havior of solutions in the limit of a small parameter related to the width of the interface (sharp interface limit). We formally derive an equation of motion of the interface, which is mean curvature motion with an additional nonlin- ear term. In a 1D model parabolic problem we rigorously justify the sharp interface limit. To this end, a special representation of solutions is introduced, which reduces analysis of the system to a single nonlinear PDE that describes the interface velocity. Further stability analysis reveals a qualitative change in the behavior of the system for small and large values of the coupling parame- ter. Using numerical simulations we also show discontinuities of the interface velocity and hysteresis. Also, in the 1D case we establish nontrivial traveling waves when the coupling parameter is large enough.",
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Sharp interface limit in a phase field model of cell motility. / Berlyand, Leonid V.; Potomkin, Mykhailo; Rybalko, Volodymyr.

In: Networks and Heterogeneous Media, Vol. 12, No. 4, 01.12.2017, p. 551-590.

Research output: Contribution to journalArticle

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