So I'm not sure how to start on this problem.

Where im having my difficulty is finding the steady state solution.

with P(x) =1

Where do I go from here?

- November 13th 2010, 12:39 AM11rdc11Help with Heat Equation with nonhomogeneous boundary conditions
So I'm not sure how to start on this problem.

Where im having my difficulty is finding the steady state solution.

with P(x) =1

Where do I go from here? - November 13th 2010, 05:12 AMJester
If you want steay state (i.e. ) then solve

subject to your BC's. - November 13th 2010, 05:18 AMzzzoak
The steady state solution depends only on x s(x).

Inserting we get

Then we find the solution

defining initial and boundary conditions to v(x,t). - November 13th 2010, 06:39 PM11rdc11

so

so

- November 13th 2010, 09:51 PM11rdc11
What would be my next step?

Separation of variables?

Case 1 -- K=0

using boundary condtions I got

so there exist no nontrivial solution

Case 2 --- K > 0

using boundary conditions also produces nontrivial solutions.

Case 3 ---- K < 0

and

and this is where I run into problems again

which just leaves me with

so my question is if

produces a nontirvial answer

for n = 0,1,2,3,...

my question is what does

have?

Can I just consider that a nontrivial solution with ?

And am I approaching the problem correctly so far? Thanks in advance - November 13th 2010, 11:31 PM11rdc11
My last step to finishing if everything is correct is to

which then gives me

- November 14th 2010, 04:39 AMJester
- November 14th 2010, 01:19 PM11rdc11
Thanks Danny,

So the correct

so

Now im not sure how to finish up. Don't know how to attempt a fourier series with the term

Do I just do the same as when I'm dealing with with ?

but instead

Once again, thanks in advance - November 14th 2010, 01:46 PMJester
Your problem is

.

The first boundary condition is a problem so we'll change this problem into a new (do-able) problem.

Let and choose and such that the new problem is

Without the source term ( ), separation of a variables would lead to what you have

Hence we look for a solution of the form

noting that we'll need a Fourier series of the form

for the source term

PS. Yes on