Advances in Differential Equations
- Adv. Differential Equations
- Volume 14, Number 5/6 (2009), 433-476.
Degenerate parabolic equation with critical exponent derived from the kinetic theory, I, generation of the weak solution
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.
Adv. Differential Equations, Volume 14, Number 5/6 (2009), 433-476.
First available in Project Euclid: 18 December 2012
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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