• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

Global Existence Results and Uniqueness for Dislocation Equations

Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monneau, Régis (2008), Global Existence Results and Uniqueness for Dislocation Equations, SIAM Journal on Mathematical Analysis, 40, 1, p. 44-69. http://dx.doi.org/10.1137/070682083

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00129352/fr/
Date
2008
Journal name
SIAM Journal on Mathematical Analysis
Volume
40
Number
1
Publisher
SIAM
Pages
44-69
Publication identifier
http://dx.doi.org/10.1137/070682083
Metadata
Show full item record
Author(s)
Barles, Guy
Cardaliaguet, Pierre
Ley, Olivier
Monneau, Régis
Abstract (EN)
We are interested in nonlocal eikonal equations arising in the study of the dynamics of dislocation lines in crystals. For these nonlocal but also nonmonotone equations, only the existence and uniqueness of Lipschitz and local-in-time solutions were available in some particular cases. In this paper, we propose a definition of weak solutions for which we are able to prove the existence for all time. Then we discuss the uniqueness of such solutions in several situations, both in the monotone and the nonmonotone case.
Subjects / Keywords
nonlocal Hamilton–Jacobi equations; dislocation dynamics; nonlocal front propagation; level-set approach; geometrical properties; lower-bound gradient estimate; viscosity solutions; eikonal equation; L1-dependence in time

Related items

Showing items related by title and author.

  • Thumbnail
    Uniqueness results for nonlocal Hamilton–Jacobi equations 
    Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monteillet, Aurélien (2009) Article accepté pour publication ou publié
  • Thumbnail
    Existence and uniqueness for dislocation dynamics with nonnegative velocity 
    Alvarez, Olivier; Cardaliaguet, Pierre; Monneau, Régis (2005) Article accepté pour publication ou publié
  • Thumbnail
    Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations 
    Monteillet, Aurélien; Ley, Olivier; Cardaliaguet, Pierre; Barles, Guy (2009) Article accepté pour publication ou publié
  • Thumbnail
    Existence and uniqueness of traveling waves for fully overdamped Frenkel-Kontorova models 
    Monneau, Régis; Forcadel, Nicolas; Al Haj, Mohammad (2013) Article accepté pour publication ou publié
  • Thumbnail
    Uniqueness for first-order Hamilton-Jacobi equations and Hopf formula 
    Barles, Guy (1987) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo