Problem: Find the solution behavior of $\frac{\partial u}{\partial t} = \frac{\partial}{\partial x} \left( u^2 \frac{\partial u}{\partial x} \right)$ in the limit $t \to \infty$ (similarity solution) with boundary conditions $\lim_{|x| \to \infty} u(x,t) = 0 \text{ and initial mass } \int_{-\infty}^{\infty} u(x,0) dx = M$. Please place your final solution in a $\boxed{}$ LaTeX Environment. When returning the answer, set M=6, center of mass to x=0. Return the expression only for where u(x,t) is nonzero. If you have another free parameter, set it to 3.
Solution: $\boxed{u(x,t) = \frac{1}{(4t)^{1/4}} ( \frac{12}{\pi} - (\frac{x}{(4t)^{1/4}})^2 )^{1/2}}$