dirk_mec1
Feb18-09, 08:17 AM
1. The problem statement, all variables and given/known data
http://img23.imageshack.us/img23/9172/14447196op1.png (http://imageshack.us)
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?
http://img23.imageshack.us/img23/9172/14447196op1.png (http://imageshack.us)
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?