Editing Heat equation (section)

=== Nonhomogeneous heat equation ===
The nonhomogeneous heat equation is
: <math>\frac{\partial u}{\partial t} = \Delta u + f</math>
for a given function <math>f = f(x,t)</math> which is allowed to depend on both {{mvar|x}} and {{mvar|t}}.{{sfn|Evans|2010|p=44}} The inhomogeneous heat equation models thermal problems in which a heat source modeled by {{mvar|f}} is switched on. For example, it can be used to model the temperature throughout a room with a heater switched on. If <math>S \subset U</math> is the region of the room where the heater is and the heater is constantly generating {{mvar|q}} units of heat per unit of volume, then {{mvar|f}} would be given by <math>f(x,t) = q 1_S(x)</math>.