Viscosity solutions for a polymer crystal growth model

Monteillet, Aurélien; Ley, Olivier; Cardaliaguet, Pierre

Monteillet, Aurélien; Ley, Olivier; Cardaliaguet, Pierre (2011), Viscosity solutions for a polymer crystal growth model, Indiana University Mathematics Journal, 60, 3, p. 895-936. http://dx.doi.org/10.1512/iumj.2011.60.4322

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00461361/fr/

Date

2011

Journal name

Indiana University Mathematics Journal

Volume

Number

Pages

895-936

Abstract (EN)

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 Hölder 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.

Subjects / Keywords

heat equation; eikonal equation; viscosity solutions; lower-bound gradient estimate; geometrical properties; level-set approach; nonlocal front propagation; Nonlocal Hamilton-Jacobi Equations