Linearized stability of traveling cell solutions arising from a moving boundary problem
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- by Y. S. Choi and Roger Lui PDF
- Proc. Amer. Math. Soc. 135 (2007), 743-753 Request permission
Abstract:
In 2003, Mogilner and Verzi proposed a one-dimensional model on the crawling movement of a nematode sperm cell. Under certain conditions, the model can be reduced to a moving boundary problem for a single equation involving the length density of the bundled filaments inside the cell. It follows from the results of Choi, Lee and Lui (2004) that this simpler model possesses traveling cell solutions. In this paper, we show that the spectrum of the linear operator, obtained from linearizing the evolution equation about the traveling cell solution, consists only of eigenvalues and there exists $\mu > 0$ such that if $\lambda$ is a real eigenvalue, then $\lambda \leq -\mu$. We also provide strong numerical evidence that this operator has no complex eigenvalue.References
- Y. S. Choi, Juliet Lee, and Roger Lui, Traveling wave solutions for a one-dimensional crawling nematode sperm cell model, J. Math. Biol. 49 (2004), no. 3, 310–328. MR 2102761, DOI 10.1007/s00285-003-0255-1
- Y. S. Choi, Patrick Groulx, and Roger Lui, Moving boundary problem for a one-dimensional crawling nematode sperm cell model, Nonlinear Anal. Real World Appl. 6 (2005), no. 5, 874–898. MR 2165218, DOI 10.1016/j.nonrwa.2004.11.005
- Mogilner, A. and D. W. Verzi (2003). A Simple 1-D Physical Model for the Crawling Nematode Sperm Cell. J. Stat. Phys. 110, 1169-1189.
Additional Information
- Y. S. Choi
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- Email: choi@math.uconn.edu
- Roger Lui
- Affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
- MR Author ID: 116795
- Email: rlui@wpi.edu
- Received by editor(s): September 3, 2004
- Received by editor(s) in revised form: September 26, 2005
- Published electronically: August 28, 2006
- Additional Notes: The first author’s research was partially supported by NIH grant no. 5P41-RR013186-07.
The second author’s research was partially supported by NSF grant no. DMS-0456570. - Communicated by: M. Gregory Forest
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 743-753
- MSC (2000): Primary 35P15; Secondary 35R35, 37L15
- DOI: https://doi.org/10.1090/S0002-9939-06-08535-2
- MathSciNet review: 2262870