Could someone tell me why is this PDE semi-linear ?
$a_{1,1}\frac{\partial^2u}{\partial x^2}+a_{1,2}\frac{\partial^2u}{\partial x\partial y }+ a_{2,1}\frac{\partial^2u}{\partial y^2}=f(x,y)\cdot u$, where $a_{i,j}$ are constants.
According to the definition of semi-linear, the above equation shouldn't be semi linear but quasi linear since the degree of the partial derivatives is 2.
Definitions:
Semi linear if the PDE is of the form $f(x_1,\dots,x_n,u,\frac{\partial u}{\partial x_1},\dots)$
Quasi linear if the PDE depends on $f(x_1,\dots,x_n,u,\frac{\partial u}{\partial x_1},\frac{\partial^2 u }{\partial x_i},\dots)$