Hi every body

i wanna to find the solution of the advection equation $\displaystyle u(x,t)$with the following intial and boundary condtion.

can it be solved by variable seperation

$\displaystyle \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial t}=0$

$\displaystyle u(x,0)=sin(kx)$ intial condition

$\displaystyle u(0,t)=sin(wt)$ boundary condition