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

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.

Quote:

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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.

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Ok, thanks for that! Cheers