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**Stability of membrane elastodynamics with applications to cylindrical aneurysms.**
*(English)*
Zbl 1330.74101

Summary: The enlargement and rupture of intracranial and abdominal aortic aneurysms constitutes a major medical problem. It has been suggested that enlargement and rupture are due to mechanical instabilities of the associated complex fluid-solid interaction in the lesions. In this paper, we examine a coupled fluid-structure mathematical model for a cylindrical geometry representing an idealized aneurysm using both analytical and numerical techniques. A stability analysis for this subclass of aneurysms is presented. It is shown that this subclass of aneurysms is dynamically stable both with and without a viscoelastic contribution to the arterial wall.

### MSC:

74K15 | Membranes |

34D20 | Stability of solutions to ordinary differential equations |

76Z05 | Physiological flows |

92C35 | Physiological flow |

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\textit{A. Samuelson} and \textit{P. Seshaiyer}, J. Appl. Math. 2011, Article ID 906475, 24 p. (2011; Zbl 1330.74101)

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### References:

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