Diffusion equation without initial conditions

[davidnr]

Hi,
How can I solve the diffusion equation in one dimension:
$$u_t=ku_{xx} ; -\infty < t < \infty , 0<x<\infty$$
With the boundary conditions:
u(0,t)= T_0 +Acos(wt)
$$u(x\rightarrow \infty,t) \rightarrow T_0$$
Thanks!

 

[Astronuc]

Hi,
How can I solve the diffusion equation in one dimension:
$$u_t=ku_{xx} ; -\infty < t < \infty , 0<x<\infty$$
With the boundary conditions:
u(0,t)= T_0 +Acos(wt)
$$u(x\rightarrow \infty,t) \rightarrow T_0$$
Thanks!

Does one maean -
$$-\infty < x < \infty , 0< t <\infty$$
I'm not sure t < 0 makes sense, unless it's a relative time.

At some large distance, T = T_o.

Try using U(x,t) = X(x)*T(t).

 

[arildno]

You might add a constant to Astronuc's trial solution.