# Greens function on half line

1. Dec 1, 2011

### maggie56

Hi, i am trying to find greens function for the heat equation with a=1, i.e du/dt - d2u/dx2 = f(x,t) for 0<x<infinty i also have the conditions, u(x,0)=0 and u(0,t)=0
When i have found my greens function i have to allow f(x,t) = delta(x-1) delta(t-1) and obtain a solution using the greens function

i have tried to do it using two different methods, one using fourier transforms and one using separation of variables, but both times i get unstuck when it comes to doing the integrals for 0 to infinity with delta functions because that is zero? I dont understand how i can work it so that i can simplify by getting rid of the delta functions, can i find the integral of negatie infinity to positive infinity and halve it or anything like that?
Any help would really be appreciated
Thanks