Find Green's function G(x,t;x',t') for the operator L = partial/partial-t - k*(partial^2 / partial-x^2) in the region...

mario99

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Find Green's function G(x,t;x,t)G(x,t;x',t') for the operator Ltk2x2\displaystyle L \equiv \frac{\partial}{\partial t} - k\frac{\partial^2}{\partial x^2} in the region {0<x<a;t>0}\{0 < x < a; t > 0 \} subject to the conditions G(0,t;x,t)=G(a,t;x,t)=0G(0,t;x',t') = G(a,t;x',t') = 0 and G(x,t;x,t)=0G(x,t;x',t') = 0 for t<tt < t'.


My attempt:

1- Does this problem depend on assumption?
2- Where is the equation to solve?
3- Are they asking for a partial or complete solution?
4- They didn't say much about xx'!
5- Is there a jump in the variable tt'? (I don't think so because it is a time variable. Am I correct?)
 
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