• 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

Fractional Keller-Segel Equation: Global Well-posedness and Finite Time Blow-up

Lafleche, Laurent; Salem, Samir (2018), Fractional Keller-Segel Equation: Global Well-posedness and Finite Time Blow-up. https://basepub.dauphine.fr/handle/123456789/18472

View/Open
KellerSegel.pdf (500.4Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01875506
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
30
Metadata
Show full item record
Author(s)
Lafleche, Laurent cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Salem, Samir
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
This article studies the aggregation diffusion equation ∂ρ/∂t = ∆^(α/2) ρ + λ div((K * ρ)ρ), where ∆^(α/2) denotes the fractional Laplacian and K = x/|x|^a is an attractive kernel. This equation is a generalization of the classical Keller-Segel equation, which arises in the modeling of the motion of cells. In the diffusion dominated case a < α we prove global well-posedness for an L^1_k initial condition, and in the fair competition case a = α for an L^1_k ∩ L ln L initial condition. In the aggregation dominated case a > α, we prove global or local well posedness for an L^p initial condition, depending on some smallness condition on the L^p norm of the initial condition. We also prove that finite time blow-up of even solutions occurs, under some initial mass concentration criteria.
Subjects / Keywords
Keller-Segel Equation; Analysis of PDEs

Related items

Showing items related by title and author.

  • Thumbnail
    p-Laplacian Keller-Segel Equation: Fair Competition and Diffusion Dominated Cases 
    Lafleche, Laurent; Salem, Samir (2018) Document de travail / Working paper
  • Thumbnail
    Infinite time blow-up in the Keller-Segel system: existence and stability 
    Davila, Juan; Del Pino, Manuel; Dolbeault, Jean; Musso, Monica; Wei, Juncheng (2019) Document de travail / Working paper
  • Thumbnail
    Existence and stability of infinite time blow-up in the Keller-Segel system 
    Davila, Juan; del Pino, Manuel; Dolbeault, Jean; Musso, Monica; Wei, Juncheng (2020) Document de travail / Working paper
  • Thumbnail
    The two-dimensional Keller-Segel model after blow-up 
    Schmeiser, Christian; Dolbeault, Jean (2009) Article accepté pour publication ou publié
  • Thumbnail
    Propagation of chaos for fractional Keller Segel equations in diffusion dominated and fair competition cases 
    Salem, Samir (2019) 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