Carpio Rodríguez, Ana María and Tapiador, B.
(2010)
*Analysis of helium bubble growth in radioactive waste.*
Nonlinear Analysis: Real World Applications, 11
(5).
pp. 4174-4184.
ISSN 1468-1218

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Official URL: http://www.sciencedirect.com/science/article/pii/S1468121810000714

## Abstract

A discrete kinetic model for the growth of helium bubbles in plutonium is proposed and analyzed. This model captures some relevant qualitative features of the time behavior of the distribution of bubble sizes. Analytic formulae for the solutions are given, which agree reasonably well with the numerical solutions, and a rigorous existence theory is established for three different equivalent formulations.

Item Type: | Article |
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Uncontrolled Keywords: | Discrete kinetic models; Integrodifferential equations; Discrete fronts; Irreversible molecular aggregation |

Subjects: | Sciences > Mathematics > Differential equations Sciences > Physics > Thermodynamics |

ID Code: | 14874 |

References: | [1] C.M. Schaldach, W.G. Wolfer, Kinetics of helium bubble formation in nuclear and structural materials, in: M.L. Grossbeck, T.R. Allen, R.G. Lott, A.S. Kumar (Eds.), Effects of Radiation Materials: 21st Symposium, ASTM STP 1447, ASTM International, West Conshohocken, 2004. [2] A.J. Schwartz, M.A. Wall, T.G. Zocco, W.G. Wolfer, Characterization and modelling of helium bubbles in self-irradiated plutonium alloys, Phil. Mag. 85 (2005) 479488. [3] A.G. McKendrick, Studies on the theory of continuous probabilities with special reference to its bearing on natural phenomena of a progressive nature, Proc. Lond. Math. Soc. 13 (1914) 401416. [4] L.L. Bonilla, A. Carpio, J.C. Neu, W.G. Wolfer, Kinetics of helium bubble formation in nuclear materials, Physica D 222 (2006) 131140. [5] A. Carpio, M.L. Rapun, Domain reconstruction by thermal measurements, J. Comput. Phys. 227 (2008) 80838106. [6] T.M. Flett, Differential Analysis, Cambridge Univ. Press, Cambridge, 1980. [7] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, Cambridge, 1991. [8] P. Linz, Linear multistep methods for Volterra integro-differential equations, J. Assoc. Comput. Mach. 16 (1969) 295301. [9] W.L. Mocarsky, Convergence of step-by-step methods for nonlinear integro-differential equations, J. Inst. Math. Appl. 8 (1971) 235239. |

Deposited On: | 19 Apr 2012 08:30 |

Last Modified: | 06 Feb 2014 10:11 |

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