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May/June 2009 Degenerate parabolic equation with critical exponent derived from the kinetic theory, I, generation of the weak solution
Takashi Suzuki a, Ryo Takahashi
Adv. Differential Equations 14(5/6): 433-476 (May/June 2009).

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.

Citation

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Takashi Suzuki a. Ryo Takahashi. "Degenerate parabolic equation with critical exponent derived from the kinetic theory, I, generation of the weak solution." Adv. Differential Equations 14 (5/6) 433 - 476, May/June 2009.

Information

Published: May/June 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1213.35077
MathSciNet: MR2502701

Subjects:
Primary: 35K55, 35Q99

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.14 • No. 5/6 • May/June 2009
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