Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Existence and nonexistence results on the radially symmetric cavitation problem


Author: François Meynard
Journal: Quart. Appl. Math. 50 (1992), 201-226
MSC: Primary 73G05; Secondary 73C50
DOI: https://doi.org/10.1090/qam/1162272
MathSciNet review: MR1162272
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Abstract: We investigate the problem of radially symmetric cavitation for a hyperelastic ball in $ \mathbb{R}{^n} , n \ge 2$. The radial equilibrium equation is analyzed by a shooting argument. The basic formulation of the problem is the same as C. A. Stuart's formulation in [10], but an asymptotic study of the solutions of the radial equilibrium equation allows us to enlarge the discussion of cavitation to cases that are excluded from the context of [10]. Finally, criteria for nonexistence to the problem of cavitation are briefly discussed. They have a physical interpretation through relations between the total energy and the radial stress.


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DOI: https://doi.org/10.1090/qam/1162272
Article copyright: © Copyright 1992 American Mathematical Society


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