Semilinear
From DispersiveWiki
A semilinear equation is a PDE of the form
where L is a linear operator and F is a nonlinear operator which does not involve any derivatives of u.
A semilinear-with-derivatives equation is a PDE of the form
where L is a linear operator, F is a nonlinear function of the first few derivatives 
, with
k strictly less than the order of L. Semilinear-with-derivatives equations are more nonlinear than semilinear equations, but are less nonlinear than quasilinear or fully nonlinear equations.
