Mass-Selection in Alignment Models with Non-Deterministic Effects

Ivano Primi, Angela Stevens, and Juan J.L. Velazquez

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Submission date: 30. Mar. 2007 (revised version: June 2007)
Pages: 37
published in: Communications in partial differential equations, 34 (2009) 5, p. 419-456 
DOI number (of the published article): 10.1080/03605300902797171
Bibtex
MSC-Numbers: 45K05, 47H10, 65M06, 65M12
Keywords and phrases: Mass selection, alignment, integro-differential equations, fix point arguments
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Abstract:
In this paper we consider an integro-differential equation model for alignment of oriented bundles of cells or filaments which includes non-deterministic effects. The reorientation of the aligning bundles of cells is described by a non-trivial probability distribution. In a paper from K. Kang, B. Perthame, A. Stevens and J.J.L. Velazquez it was shown that the long time behavior of a related deterministic model aligns the bundles into two opposite directions, but the masses are not balanced. Here we show that the probabilistic effects result in a selection of masses, namely exactly balanced for two opposite directions or accumulation into one direction only.