- #1
wumple
- 60
- 0
Homework Statement
Is the operator
Lu = du/dx + u * du/dy
linear?
Homework Equations
Linearity occurs for L[u+cv] = L + cL[v]
The Attempt at a Solution
I know this isn't linear because of the second term, but I don't understand why I can't write the operator as
L = (d/dx + u * d/dy)
which then seems to almost work out, except that I don't know what to make 'u' in the operator when applying the linearity condition since the linearity condition uses two different functions instead of only 'u'.