Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 261, pp. 1-14.

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

Authors: Xuhuan Zhou  (Zhejiang Univ., Hangzhou, China)
         Weiliang Xiao (Nanjing Univ. of Finance and Econ., Nanjing, China)
         Taotao Zheng (Zhejiang Univ. of Science and Tech., Hangzhou, China)

Abstract: 
 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 07, 2015.
Math Subject Classifications: 35K15, 35K55, 35Q35, 76S05.
Key Words: Generalized porous medium equation;  well-posedness;
           blowup criterion; Besov spaces.