Viscosity solutions for a polymer crystal growth model

Abstract : We prove existence of a solution for a polymer crystal growth model describing the movement of a front $(\Gamma(t))$ evolving with a nonlocal velocity. In this model the nonlocal velocity is linked to the solution of a heat equation with source $\delta_\Gamma$. The proof relies on new regularity results for the eikonal equation, in which the velocity is positive but merely measurable in time and with H\"{o}lder bounds in space. From this result, we deduce \textit{a priori} regularity for the front. On the other hand, under this regularity assumption, we prove bounds and regularity estimates for the solution of the heat equation.
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Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2011, 60 (3), pp.895-936
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Dernière modification le : mercredi 12 juillet 2017 - 01:15:41
Document(s) archivé(s) le : vendredi 18 juin 2010 - 22:18:22

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  • HAL Id : hal-00461361, version 1
  • ARXIV : 1003.1059

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Pierre Cardaliaguet, Olivier Ley, Aurélien Monteillet. Viscosity solutions for a polymer crystal growth model. Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2011, 60 (3), pp.895-936. <hal-00461361>

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