- #1
richyw
- 180
- 0
Homework Statement
Solve the Dirichlet problem for the heat equation
[tex]u_y=u_{xx}\quad 0<x<2\pi, \: t>0[/tex][tex]u(x,0)=\cos x[/tex][tex]u(0,t)=u(2\pi,t)=e^{-t}[/tex]
Homework Equations
The Attempt at a Solution
I have no idea what to do here. It seems to me like it's a mix of the solutions we learned. I have time-dependant boundary conditions, and then an initial condition. To solve this do I have to use the reference temperature to turn it into an inhomogenous equation with homogenous boundary conditions, and then the eigenfunction expansion method, or is there an easier way?