Viscosity solutions for a polymer crystal growth model
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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00461361/fr/Date
2011Journal name
Indiana University Mathematics JournalVolume
60Number
3Pages
895-936
Publication identifier
Metadata
Show full item recordAbstract (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 EquationsRelated items
Showing items related by title and author.
-
Monteillet, Aurélien; Ley, Olivier; Cardaliaguet, Pierre; Barles, Guy (2009) Article accepté pour publication ou publié
-
Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monteillet, Aurélien (2009) Article accepté pour publication ou publié
-
Cardaliaguet, Pierre; Rainer, Catherine (2011) Article accepté pour publication ou publié
-
Biton, Samuel; Cardaliaguet, Pierre; Ley, Olivier (2008) Article accepté pour publication ou publié
-
Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monneau, Régis (2008) Article accepté pour publication ou publié