Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type

Abstract : We study two toy models obtained after a slight modification of the nonlinearity of the usual doubly parabolic Keller-Segel system. For these toy models, both consisting of a system of two parabolic equations, we establish that for data which are, in a suitable sense, smaller than the diffusion parameter τ in the equation for the chemoattractant, we obtain global solutions, and for some data larger than τ , a finite time blowup. In this way, we check that our size condition for the global existence is sharp for large τ , up to a logarithmic factor.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03699868
Contributor : Alexandre Boritchev Connect in order to contact the contributor
Submitted on : Monday, June 20, 2022 - 3:44:18 PM
Last modification on : Wednesday, June 22, 2022 - 3:35:38 AM

Files

KS-large-solutions-paper 2 Sub...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03699868, version 1
  • ARXIV : 2206.10399

Citation

Piotr Biler, Alexandre Boritchev, Lorenzo Brandolese. Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type. 2022. ⟨hal-03699868⟩

Share

Metrics

Record views

0

Files downloads

0