Viscosity solutions for a polymer crystal growth model

2010/03/04 by Pierre Cardaliaguet, Cardaliaguet, Pierre, Olivier Ley +3 · 1 citation
Mathematics · #35A05 #35B50 #35D05 #35F25 #45G10 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35A05 #msc:35B50 #msc:35D05 #msc:35F25 #msc:45G10 #msc:49L25

paper · pdf · doi:10.48550/arxiv.1003.1059

arxiv created 2010/03/04 · arxiv updated 2010/03/05

Abstract

We prove existence of a solution for a polymer crystal growth model describing the movement of a front (Γ(t)) evolving with a nonlocal velocity. In this model the nonlocal velocity is linked to the solution of a heat equation with source δ_Γ. 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 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.

Cited by

• A free boundary problem in accretive growth

Related

• On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion
• Weak sequential stability of solutions to a nonisothermal kinetic model for incompressible dilute polymeric fluids
• Long-time behavior for a nonlocal model from directed polymers
• Analysis of a viscosity model for concentrated polymers
• Convergence of a scheme for a one dimensional nonlocal and nonlinear eikonal equation