===== PDE 4: Porous medium equation =====
Here we consider the equation
 \[u_t =(u^m u_x)_x \]
either as an initial value problem or a two-sided initial/boundary value problem,  e.g.  \(u(0,t)=g_0(t)\),  \(u(1,t)=g_1(t)\),  \(u(x,0)=f(x)\). Find relevant values for \(m\) in the literature. 

**Google** Porous medium equation, mesa problem, Barenblatt solution

**Challenges** Non-linearity, applications.