- #1
idraftscience
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Homework Statement
Solve
[itex]\frac{\partial v}{\partial t} = k\frac{\partial^2 v}{\partial x^2} - v
[/itex]
[itex] 0\leq x \leq L [/itex]
[itex] t > 0 [/itex]
Homework Equations
[itex] v(x,0) = f(x), v(0,t)=0, \frac{\partial v}{\partial x}(L,t) = -v(L,t) [/itex]
The Attempt at a Solution
I've already attempted to solve this using separation of variables, but I'm not sure if that is a valid approach as the equation is not homogeneous (?) due to the v(x,0) = f(x) term. I've also attempted using green's theorem but I keep getting stuck, though this may be due to a math error. Can anyone give me any insight as to where I may be going wrong?