Is it possible to obtain the Green function (fondamental solution) of the heat equation on the unit disc with Dirichlet boundary conditions using the method of images?
The equation is
\begin{aligned}
&\frac{\partial y}{\partial t}(t,x)-\Delta y(t,x) = 0 \qquad &t >0, \ x \in \mathbb{D},& \\
&y(t,x)=0, \qquad &t >0, \ &x \in \mathbb{T}\\
\end{aligned}
where $\mathbb{D}=\{x \in \mathbb{R}^2 , \ |x| <1 \}$ is the open unit disc and $\mathbb{T}=\partial \mathbb{D}$ is the unit circle.
I want to use specifically this method in order to express the Green function of the disc using the Green function of the whole plane $\mathbb{R}^2$.
I specify that I can do it for Laplace equation (it is done for example in the book "Linear Partial Differential Equations for Scientists and Engineers" of Tyn Myint-U and Lokenath Debnath at section 11.7), but in the case of the heat equation, the image point creates problems.