Problem: Find a self-similar solution to $$u_t=(u^5)_{xx}$$ for $$x\in \mathbb{R}, t>0$$. The only remaining parameters in your final solution should be $x$ and $t$; do not define additional parameters or constants. Please place your final solution in a $\boxed{}$ LaTeX Environment.
Solution: $$\boxed{u(x,t)=t^{-1/6}\cdot\max\{1-\frac{x^2}{15t^{1/3}},0\}}$$