Find the solutions to in two and three dimensions subject to the following boundary conditions

(a) for and for

(b) for and for

Note that the boundary conditions do not depend on or (in 3D)

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- Oct 7th 2010, 08:16 PMJimmy_WI don't know how to start this one
Find the solutions to in two and three dimensions subject to the following boundary conditions

(a) for and for

(b) for and for

Note that the boundary conditions do not depend on or (in 3D) - Oct 8th 2010, 04:28 AMJester
Since the boundary conditions are independent of or and , I might suggest switching the PDEs into polar coordinates and looking for solution in terms of the radius only.

- Oct 18th 2010, 04:15 AMJimmy_W
I'm having trouble understanding exactly what the initial conditions are saying here.

If I had to solve this PDE with conditions (another question I have):

I would do it as follows:

Assume :

So

and

Solving these,

and

and so

.........(Eqn 1)

Then applying all conditions and skipping a few steps the solution is

But I'm getting confused with the initial conditions here, and how to go from Eqn (1) onwards with the intitial conditions onwards i.e.

(a) for and for

(b) for and for

For the 3d case, I have

Assume

Then

Dividing through

Which results in 3 ODE's

which have solutions

So, due to superposition,

which is all I have...I don't understand the form of the initial conditions. - Oct 18th 2010, 04:16 AMJimmy_W