Linearization of PDE

1. Feb 18, 2009

dirk_mec1

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:

$$F'(u)= \left( 2u \frac{ \partial{u} }{ \partial{x} } + \frac{ \partial{} }{ \partial{u} } \frac{ \partial{u} }{ \partial{x} } +\frac{ \partial{^2 u} }{ \partial{x^2} } + u \frac{ \partial{} }{ \partial{u} } \frac{ \partial{^2} }{ \partial{x^2} } u \right) v \longrightarrow$$

$$\frac{\partial{v}}{ \partial{t}} =\frac{\partial{v}}{ \partial{x}} + \frac{\partial{^2v}}{ \partial{x^2}}$$

Is this correct?

Last edited by a moderator: May 4, 2017