Advances in Differential Equations

Degenerate parabolic equation with critical exponent derived from the kinetic theory, I, generation of the weak solution

Takashi Suzuki a and Ryo Takahashi

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Abstract

We study a degenerate parabolic equation derived from the kinetic theory using Rényi-Tsallis entropy. If the exponent is critical, we have the threshold mass for the blowup of the solution and also the finiteness of type II blowup points. These results extend some facts on the Smoluchowski-Poisson equation associated with the Boltzmann entropy in two space dimensions and actually, we use mass quantization of the blowup family of stationary solutions for the proof. In this first paper, we show local in time existence of the weak solution.

Article information

Source
Adv. Differential Equations Volume 14, Number 5/6 (2009), 433-476.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867256

Mathematical Reviews number (MathSciNet)
MR2502701

Zentralblatt MATH identifier
1213.35077

Subjects
Primary: 35K55: Nonlinear parabolic equations 35Q99: None of the above, but in this section

Citation

Suzuki a, Takashi; Takahashi, Ryo. Degenerate parabolic equation with critical exponent derived from the kinetic theory, I, generation of the weak solution. Adv. Differential Equations 14 (2009), no. 5/6, 433--476. https://projecteuclid.org/euclid.ade/1355867256.


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