Electron. J. Diff. Equ., Vol. 2015 (2015), No. 261, pp. 1-14.

Well-posedness and blowup criterion of generalized porous medium equation in Besov spaces

Xuhuan Zhou, Weiliang Xiao, Taotao Zheng

We study the generalized porous medium equation of the form $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$ where P is an abstract operator. We obtain the local well-posedness in Besov spaces for large initial data, and show the solution becomes global if the initial data is small. Also, we prove a blowup criterion for the solution.

Submitted June 25, 2015. Published October 7, 2015.
Math Subject Classifications: 35K15, 35K55, 35Q35, 76S05.
Key Words: Generalized porous medium equation; well-posedness; blowup criterion; Besov spaces.

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  Xuhuan Zhou
Department of Mathematics, Zhejiang University
Hangzhou 310027, China
email: zhouxuhuan@163.com
Weiliang Xiao
chool of Applied Mathematics
Nanjing University of Finance and Economics
Nanjing 210023, China
email: xwltc123@163.com
  Taotao Zheng
Department of Mathematics
Zhejiang University of Science and Technology
Hangzhou 310023, China
email: taotzheng@126.com

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