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Article
Linearized Stability of Traveling Cell Solutions Arising from a Moving Boundary Problem
Proceedings of the American Mathematical Society
  • Y. S. Choi
  • Roger Lui, Worcester Polytechnic Institute
Document Type
Article
Publication Date
3-1-2007
Disciplines
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. laments 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 μ > 0 such that if λ is a real eigenvalue, then λ <= -μ. We also provide strong numerical evidence that this operator has no complex eigenvalue.
DOI
10.1090/S0002-9939-06-08535-2
Publisher Statement
First published in Proceedings of the American Mathematical Society in 135(3), published by the American Mathematical Society.
Citation Information
Y. S. Choi and Roger Lui. "Linearized Stability of Traveling Cell Solutions Arising from a Moving Boundary Problem" Proceedings of the American Mathematical Society Vol. 135 Iss. 3 (2007) p. 743 - 753
Available at: http://works.bepress.com/roger_lui/2/