Solving Diffusion Equation with Boundary Conditions

[tirwit]

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).

Homework Equations

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.

 

[LCKurtz]

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?