Solution of the anisotropic porous medium equation in $R^n$ under an $L^1$-initial value

Huaiyu Jian, Binheng Song

Consider the anisotropic porous medium equation, $u_t=\sum _{i=1}^n(u^{m_i}{)}_{x_i{x}_i},$ where $m_i>0,(i=1,2,...,n)$ satisfying $\underset{1\le i\le n}{\min }\{m_i\}\le 1,$ $\sum…