Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 18 min ago
Peer-reviewedCC BYAnnals of PDE

Existence of Finite Time Blow-Up in Keller-Segel System

  • Federico Buseghin1
  • Juan Dávila1
  • Manuel A. del Pino1
  • Monica Musso1
  1. 1Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
Open at sourceDOICite

Abstract

Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system { ut =& Δ u − ∇ · (u ∇ v) in ℝ2× (0,T), v =& (−Δ ℝ2)−1 u := 1/(2π ) ∫ ℝ2 log 1/(|x−z|) u(z,t) dz, & u(· ,0) = u0⋆ ≥ 0 in ℝ2. . u t = Δ u - ∇ · ( u ∇ v ) in R 2 × ( 0 , T ) , v = ( - Δ R 2 ) - 1 u : = 1 2 π ∫ R 2 log 1 | x - z | u ( z , t ) d z , u ( · , 0 ) = u

Related

  1. Existence, Uniqueness, Feller Property and Diricihlet form of the Keller-Segel particle system up to blow up
    Yoan Tardy
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  2. Global existence of weak solutions in a Keller-Segel system with local anisotropy and nonlinear diffusion
    Max Hegenbart
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Optimal strong convergence of a splitting mixed finite element method for a stochastic Keller--Segel system
    Liet Vo
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingProbabilityarXiv
  4. A Li-Yau and Aronson-Bénilan approach for the Keller-Segel system with critical exponent
    Charles Elbar, Alejandro Fernández-Jiménez, Filippo Santambrogio
    HALPreprintLicence not statedAnalysis & PDEsHAL
  5. A posteriori error estimates for a finite volume approximation of a local sensing Keller-Segel model
    Niklas Kolbe, Kiwoong Kwon
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@article{buseghin2026existence,
  title = {{Existence of Finite Time Blow-Up in Keller-Segel System}},
  author = {Federico Buseghin and Juan Dávila and Manuel A. del Pino and Monica Musso},
  journal = {Annals of PDE},
  year = {2026},
  month = may,
  doi = {10.1007/s40818-026-00241-7},
  url = {https://doi.org/10.1007/s40818-026-00241-7},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Existence of Finite Time Blow-Up in Keller-Segel System
AU  - Federico Buseghin
AU  - Juan Dávila
AU  - Manuel A. del Pino
AU  - Monica Musso
PY  - 2026
DA  - 2026/05/16
JO  - Annals of PDE
DO  - 10.1007/s40818-026-00241-7
UR  - https://doi.org/10.1007/s40818-026-00241-7
AB  - Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system { u_t =& Δ u − ∇ · (u ∇ v) in ℝ^2× (0,T), v =& (−Δ _ℝ^2)^−1 u := 1/(2π ) ∫ _ℝ^2 log 1/(|x−z|) u(z,t) dz, & u(· ,0) = u_0^⋆  ≥ 0 in ℝ^2. . u t = Δ u - ∇ · ( u ∇ v ) in R 2 × ( 0 , T ) , v = ( - Δ R 2 ) - 1 u : = 1 2 π ∫ R 2 log 1 | x - z | u ( z , t ) d z , u ( · , 0 ) = u
SN  - 2199-2576
SN  - 2524-5317
ER  -