Hey all, i got a question im struggling with, and as of yet, i havent got anywhere..

It is a follows:

Determine a function $\displaystyle u: [0,\pi] \times [0,\infty[-> R

$ such that $\displaystyle

\frac{du}{dt} (x,t)-\frac{d^2u}{dx^2}(x,t) =0$

$\displaystyle , t<0,x\in]0,\pi[ $ $\displaystyle

u(x,0)=sin(x)cos^2(x), x \in [0,\pi] $ $\displaystyle

u(0,t)=0, u(\pi,t)=0, t>0$

Any help/tips/hints or guides is appreciated