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Math Help - Partial differential equation problem

  1. #1
    LHS
    LHS is offline
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    Exclamation 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:


    Any help would be greatly appreciated!
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  2. #2
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    Re: Partial differential equation problem

    Quote Originally Posted by LHS View Post
    '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:


    Any help would be greatly appreciated!
    .
    Follow Math Help Forum on Facebook and Google+

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