The flow of heat in a given circle of radius R is given as: $$ \frac{\partial T}{\partial t} = \kappa \nabla ^2 T $$ Where $T(r=R,\theta, t) = T_0 sin^2(2\theta)$ and the starting temperature is $T(r,\theta, t=0) = T_0$
Find the stationary temperature $(T_s = (r,\theta))$ that we expect to get after long times, $t\to \infty$
I'm having difficulties understanding the question. I understand that for stationary solutions, we know the solution is not dependent on time, so does left hand side become 0? If so, what exactly do with the initial starting temperature? $(T_0)$