# Solving Diffusion Equation with Boundary Conditions

• tirwit
In summary, the problem is to obtain the solution of the diffusion equation with boundary conditions of u(t,0)=u1, u(t,l)=u2, and u(0,x)=u1+(u2-u1)x/l+a.sin(n\pix/l) in the semi-plane x > 0, with additional condition of u(t,0)=u0+a.sin(\omegat). The subjects that may be useful in solving this problem can be found in Riley's "Mathematical Methods for Physics and Engineering" and Zill's "Advanced Engineering Mathematics".

## Homework Statement

Obtain the solution of the diffusion equation, u(t,x)

a) satisfying the boundary conditions:
u(t,0)=u1, u(t,l)=u2, u(0,x)=u1+(u2-u1)x/l+a.sin(n$$\pi$$x/l);

b) in the semi-plane x > 0, with u(t,0)=u0+a.sin($$\omega$$t).

Wish I knew...

## The Attempt at a Solution

I haven't done none because I don't know where to start. I just want to ask what should I study to solve this problem. I have Riley's "Mathematical Methods for Physics and Engineering" and Zill's "Advanced Engineering Mathematics". If you have and can point me out the chapters, I would be much appreciated, or you can just tell me the subjects, that I'll try and look for them in the books.

tirwit said:

## Homework Statement

Obtain the solution of the diffusion equation, u(t,x)

It is good form to give the diffusion equation in case anyone that might help you doesn't remember it exactly and doesn't have their PDE book handy.

a) satisfying the boundary conditions:
u(t,0)=u1, u(t,l)=u2, u(0,x)=u1+(u2-u1)x/l+a.sin(n$$\pi$$x/l);

That last equation looks strange. What is n? There is usually no "n" in the BC. Are you sure you have stated the original problem correctly?