Uniform L boundedness for a degenerate parabolic-parabolic Keller-Segel model


Journal Article

This paper investigates the existence of a uniform in time L∞ bounded weak entropy solution for the quasilinear parabolic-parabolic KellerSegel model with the supercritical diffusion exponent 0 < m < 2 - 2/d in the multi-dimensional space ℝd under the condition that the L d(2-m)/2 norm of initial data is smaller than a universal constant. Moreover, the weak entropy solution u(x,t) satisfies mass conservation when m > 1-2/d. We also prove the local existence of weak entropy solutions and a blow-up criterion for general L1 ∩ L∞ initial data.

Full Text

Duke Authors

Cited Authors

  • Cong, W; Liu, JG

Published Date

  • March 1, 2017

Published In

Volume / Issue

  • 22 / 2

Start / End Page

  • 307 - 338

International Standard Serial Number (ISSN)

  • 1531-3492

Digital Object Identifier (DOI)

  • 10.3934/dcdsb.2017015

Citation Source

  • Scopus