# PDE with a Dirac Delta function as boundary condition

I would like to have some information how to solve this PDE: $\partial_tu(x,t)=k^2\partial_{xx}u(x,t)$ with the following boundary and initial conditions: $u(x,0)=u_0(x)$,$u(0,t)=\delta(t-t_0)$,$u(L,t)=u_L(t)$ Thanks.

• You mean "you would like to know how to solve this PDE ... under the boundary and initial conditions..."? I juust want to understand your question please. – al-Hwarizmi Jul 16 '13 at 9:24
• And adding your own thoughts is welcome, too – TZakrevskiy Jul 16 '13 at 9:24
• What did block you? Have you already used, for example, separation of variables? – Avitus Jul 16 '13 at 9:26
• @al-Hwarizmi: just corrected the question. Just a mistake – Riccardo.Alestra Jul 16 '13 at 9:31