- #1

Thomas Moore

- 12

- 2

For example, for the wave equation, we have: u_{xx} + u_{yy} = 0, where a subscript denotes a partial derivative.

So, my textbook says to write:

$L = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}$

And then it is easy to deduce that $L(u+v) = L(u) + L(v)$ and $L(c u) = cL(u)$.

But, I have no idea how to do this for the following PDEs:

1. $u_{t} - u_{xx} + u/x = 0$, the $u/x$ is throwing me off.

2. $u_{tt} - u_{xx} + u^3 = 0$, the $u^3$ term is throwing me off.

I don't know how to write this as $Lu = 0$, to determine linearity. Any help would be appreciated, thanks!