- Thread starter
- #1

$\begin{aligned}

{{u}_{t}}&=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\

{{u}_{x}}(0,t)&=0,\text{ }{{u}_{x}}(L,t)=0,\text{ for }t>0, \\

u(x,0)&=6+\sin \frac{3\pi x}{L}

\end{aligned}$

2) Transform the problem so that the boundary conditions get homogeneous:

$\begin{aligned}

{{u}_{t}}&=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\

{{u}_{x}}(0,t)&=Ae^{-at},\text{ }{{u}_{x}}(L,t)=B,\text{ for }t>0, \\

u(x,0)&=0

\end{aligned}$

__Attempts__:

1) No ideas for this one, I don't know how to proceed when the initial conditions have the first derivative.

2) I think I need to define a new function right? But how?