Math @ Duke

Publications [#329169] of JianGuo Liu
Papers Published
 Cong, W; Liu, JG, Uniform L^{∞} boundedness for a degenerate parabolicparabolic KellerSegel model,
Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 2
(March, 2017),
pp. 307338, American Institute of Mathematical Sciences (AIMS) [doi]
(last updated on 2019/06/20)
Abstract: This paper investigates the existence of a uniform in time L∞ bounded weak entropy solution for the quasilinear parabolicparabolic KellerSegel model with the supercritical diffusion exponent 0 < m < 2  2/d in the multidimensional space ℝd under the condition that the L d(2m)/2 norm of initial data is smaller than a universal constant. Moreover, the weak entropy solution u(x,t) satisfies mass conservation when m > 12/d. We also prove the local existence of weak entropy solutions and a blowup criterion for general L1 ∩ L∞ initial data.


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