Heat equation on a circular plate

Question

I'm in trouble with the following problem: assuming a circular plate of radius $R$, the heat equation on it, is: $$\partial_t u(\rho,\phi,t)=k\left(\partial_{\rho\rho}u(\rho,\phi,t)+\frac{1}{r}\partial_\rho(\rho,\phi,t)+\frac{1}{\rho^2}\partial_{\phi\phi}u(\rho,\phi,t)\right)$$ with $$\rho\le R,0\le\phi\le 2\pi$$ Assuming: $u(\rho,\phi,0)=u_0$, $u(0,0,t)=\delta(t-kt_0)$ with $k\in\mathbb{N}$, $u(R,\phi,t)=u_0$, what is the solution of the heat equation in this case? Thanks