Author:
Cucchi Alessandro,Mellet Antoine,Meunier Nicolas
Abstract
<p style='text-indent:20px;'>In this paper, we prove the existence of traveling wave solutions for an incompressible Darcy's free boundary problem recently introduced in [<xref ref-type="bibr" rid="b6">6</xref>] to describe cell motility. This free boundary problem involves a nonlinear destabilizing term in the boundary condition which describes the active character of the cell cytoskeleton. By using two different methods, a constructive method via a graph analysis and a local bifurcation method, we prove that traveling wave solutions exist when the destabilizing term is strong enough.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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