# Partial differential equation problem

• Jan 26th 2011, 03:16 PM
LHS
Partial differential equation problem
'Show that the heat equation has complex-valued solutions of the form
F(x) exp(iwt) provided that kF′′ = iwF. Find F if F(x) tends to 0 as x tends to 1 and F(0) = A, where A is a real constant.'

I can show the first part of this, but i'm having issues with the next bit, what I get must be wrong, because I can't seem to split it into real and imaginary for the second part of the question

'Let T(x, t) be the real part of F(x) exp(iwt). Verify that:
http://img585.imageshack.us/img585/2154/41308828.png

Any help would be greatly appreciated!
• Jun 28th 2011, 12:54 AM
Sudharaka
Re: Partial differential equation problem
Quote:

Originally Posted by LHS
'Show that the heat equation has complex-valued solutions of the form
F(x) exp(iwt) provided that kF′′ = iwF. Find F if F(x) tends to 0 as x tends to 1 and F(0) = A, where A is a real constant.'

Are you sure about the highlighted part? If "F(x) tends to 0 as x tends to infinity" then the given solution can be obtained.

I can show the first part of this, but i'm having issues with the next bit, what I get must be wrong, because I can't seem to split it into real and imaginary for the second part of the question

'Let T(x, t) be the real part of F(x) exp(iwt). Verify that:
http://img585.imageshack.us/img585/2154/41308828.png

Any help would be greatly appreciated!

.