It hasn't disappeared. The first equation can be expressed in the form of the second by susbsituting:
h(x, y, u) = f(x, y) - c(x, y) u
In a semi-linear equation there is no constraint that the function "h" needs to be linear in u.
Hi Folks,
Semi Linear PDE
A book book gives a linear first order PDE in the form
a(x,y)u_x+b(x,y)u_y+c(x,y)u=f(x,y)
My lectures notes has a 'semi linear' PDE in the form
a(x,y)u_x+b(x,y)u_y=h(x,y,u)
The presence of u on the RHS makes the PDE semi linear however where does the independant variable u itself disappear in the second equation?
Thanks