One-Dimensional Heat Equation Problem

[HansLee]

Hi, I need help to solve this problem, about 1-D heat equation

\partialu / \partialt = k (\partial²u / \partialx²)-2u (0< x <1)

u(x,0)=e^-x
u(0,t)=e^-2t
u(1,t)=0

I need to solve it with separation variable

 

[Office_Shredder]

Ok... what have you done so far? Do you know how to start a problem like this?

 

[HansLee]

No, I have no idea how to start it, bcos it's non-homogeneous eq, can u help me?

 

[Office_Shredder]

I just realized that you don't actually have the heat equation in your first post. There should be no -2u term in the equation. Can you verify what you're supposed to be solving?

If you're actually trying to solve the heat equation, then start with u(x,t) = X(x)T(t) for some X and T functions and then try to separate the x's and the t's

 

[HallsofIvy]

Even with the "-2u" term, do exactly what Office Shredder says, just what you would normally do to "separate variables"- let u(x,t)= X(x)T(t) and put into the equation:

X\frac{du}{dt}= \kappa T\frac{d^2X}{dx^2}- 2XT

divided through by XT and see what happens.