A linear partial differential equation is a partial differential equation for which the expression involving the unknown function and all of its derivatives defines a linear operator. It can be written
 |
where 
is a linear operator whose
coefficients depend only on the independent variables and 
is a given function. The equation is homogeneous when 
. Solutions of a homogeneous linear partial differential
equation obey the superposition principle.
Examples include Laplace's equation, the heat conduction equation, and the wave
equation (Evans 2010).
