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Linearization of PDE

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img23.imageshack.us/img23/9172/14447196op1.png [Broken]

    3. The attempt at a solution

    I found after linearization:

    [tex]F'(u)= \left( 2u \frac{ \partial{u} }{ \partial{x} } + \frac{ \partial{} }{ \partial{u} } \frac{ \partial{u} }{ \partial{x} } +\frac{ \partial{^2 u} }{ \partial{x^2} } + u \frac{ \partial{} }{ \partial{u} } \frac{ \partial{^2} }{ \partial{x^2} } u \right) v \longrightarrow [/tex]

    [tex] \frac{\partial{v}}{ \partial{t}} =\frac{\partial{v}}{ \partial{x}} + \frac{\partial{^2v}}{ \partial{x^2}}[/tex]

    Is this correct?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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