Viscosity solutions for a polymer crystal growth model

Details Viscosity solutions for a polymer crystal growth model Viscosity solutions for a polymer crystal growth model

2010-03-04

arxiv.org/abs/1003.1059v1

Mathematics

Analysis of PDEs

Scientific paper

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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