# PDE equation how to sole?

Let the ends of a copper rod 100cm long be maintained at 0C. Suppose that the center of the bar is heated to 100C by an external heat source and that this situation is maintained until a steady state results. Find this steady-state temperature distribution.

i know that two separate boundary-value problems on the rod from 0 to 50 cm and on the rod from 50 to 100cm. For the rod from 0 to 50 cm, T1 = 0, T2 = 100, and L = 50 therefore

v(x) = (T2 − T1)/L *x + T1 = 2x, 0 < x < 50. @

For the rod from 50 to 100 cm, @

T1 = 100, T2 = 0, and L = 50 therefore@

v(x) = (T2 − T1)/L*(x − 50)+ T1 = 200 − 2x, 50 < x < 100.@

and then how can solve it? there isn't initial condition f(x)

• You don't need an initial condition to find the steady state. – ultrainstinct Dec 16 '17 at 9:53
• why?? i dont understand that – kim Dec 16 '17 at 12:28
• Please format your post with MathJax! People will be more likely to respond. – DaveNine Dec 16 '17 at 19:26
• @kim Because the steady state is what happens really far into the future, it's independent of what the rod initially looked like. – ultrainstinct Dec 16 '17 at 20:38