Hi. I'm trying to solve the heat equation with the initial boundary conditions:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]u(0,t)=f_1(t)[/tex]

[tex]u(x_1,t)=f_2(t)[/tex]

[tex]u(x,0)=f(x)[/tex]

[tex]0<x<x_1[/tex]

[tex]t>0[/tex]

And the heat equation: [tex]\frac{\partial u}{\partial t}-k\frac{\partial^2 u}{\partial x^2}=0[/tex]

So when I make separation of variables I get:

[tex]\nu=X(x)T(t)[/tex]

[tex]\frac{T'(t)}{T(t)}=k\frac{X''(x)}{X(x)}[/tex]

Then I have to solve for X

[tex]kX''(x)-\lambda X(x)=0[/tex]

With the initial boundary conditions

[tex]X(0)=f_1(t)[/tex]

[tex]X(x_1)=f_2(t)[/tex]

And for T:

[tex]T'(t)-\lambda T(t)=0[/tex]

With initial value:

[tex]T(0)=f(x)[/tex]

How should I proceed from here? I'm not sure how to make this accomplish the boundary conditions.

Bye, thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Heat equation with boundary conditions

**Physics Forums | Science Articles, Homework Help, Discussion**