• 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

Non-existence of global characteristics for viscosity solutions

Roos, Valentine (2018), Non-existence of global characteristics for viscosity solutions. https://basepub.dauphine.fr/handle/123456789/17960

View/Open
VarViscDiff.pdf (409.3Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01827656
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
26
Metadata
Show full item record
Author(s)
Roos, Valentine
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Two different types of generalized solutions, namely viscosity and variational solutions, were introduced to solve the first-order evolutionary Hamilton–Jacobi equation. They coincide if the Hamiltonian is convex in the momentum variable. In this paper we prove that there exists no other class of integrable Hamiltonians sharing this property. To do so, we build for any non-convex non-concave integrable Hamiltonian a smooth initial condition such that the graph of the viscosity solution is not contained in the wavefront associated with the Cauchy problem. The construction is based on a new example for a saddle Hamiltonian and a precise analysis of the one-dimensional case, coupled with reduction and approximation arguments.
Subjects / Keywords
viscosity solutions; Hamilton–Jacobi equation

Related items

Showing items related by title and author.

  • Thumbnail
    Solutions variationnelles et solutions de viscosité de l'équation de Hamilton-Jacobi 
    Roos, Valentine (2017-06-30) Thèse
  • Thumbnail
    Existence of global strong solution for Korteweg system in one dimension for strongly degenerate viscosity coefficients 
    Burtea, Cosmin; Haspot, Boris (2022) Article accepté pour publication ou publié
  • Thumbnail
    New effective pressure and existence of global strong solution for compressible Navier-Stokes equations with general viscosity coefficient in one dimension 
    Burtea, Cosmin; Haspot, Boris (2020) Article accepté pour publication ou publié
  • Thumbnail
    Existence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system 
    Haspot, Boris; Charve, Frédéric (2013) Article accepté pour publication ou publié
  • Thumbnail
    Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D 
    Haspot, Boris (2018) 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