#### Document Type

Article

#### Publication Date

3-1-2007

#### Publication Title

Proceedings of the American Mathematical Society

#### 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.

#### Suggested Citation

Choi, Y. S.
, Lui, Roger
(2007). Linearized Stability of Traveling Cell Solutions Arising from a Moving Boundary Problem. *Proceedings of the American Mathematical Society, 135*(3), 743-753.

Retrieved from:
https://digitalcommons.wpi.edu/mathematicalsciences-pubs/25

#### Volume

135

#### Issue

3

#### First Page Number

743

#### Last Page Number

753

#### 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.