Global solutions for an age-dependent model of nucleation, growth and ageing with hysteresis

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May 2010, 13(3): 517-535. doi: 10.3934/dcdsb.2010.13.517

Global solutions for an age-dependent model of nucleation, growth and ageing with hysteresis

Youssef Amal ^1, and Martin Campos Pinto ^2,

1.	Université de Strasbourg et CNRS, C.G.S., 1 rue Blessig, 67084 Strasbourg Cedex, France
2.	Université de Strasbourg et CNRS, I.R.M.A., 7 rue René Descartes, 67084 Strasbourg Cedex, France

Received September 2008 Revised May 2009 Published February 2010

Abstract
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In this article we establish the global well-posedness of a recent model proposed by Noguera, Fritz, Clément and Baronnet for simultaneously describing the process of nucleation, growth and ageing of particles in thermodynamically closed and initially supersaturated systems. This model, which applies to precipitation in solution, vapor condensation and crystallization from a simple melt, can be seen as a highly nonlinear age-dependent population problem involving a delayed birth process and a hysteresis damage operator.

Keywords: Age-dependent growth model, existence of global solutions., integral equations, hysteresis.

Mathematics Subject Classification: Primary: 35A05, 45G; Secondary: 47J40, 92D2.

Citation: Youssef Amal, Martin Campos Pinto. Global solutions for an age-dependent model of nucleation, growth and ageing with hysteresis. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 517-535. doi: 10.3934/dcdsb.2010.13.517

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