# Math Help - Form of Semi Linear Linear PDE's

1. ## Form of Semi Linear Linear PDE's

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

2. 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.

3. Originally Posted by Matt Westwood
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.
Ok, thanks for that! Cheers