Source term in a partial differential equation
= Source term in a partial differential equation
{title2=$f(x,t)$}
= PDE source term
{c}
{synonym}
A prescribed <PDE source term> changes the <heat equation> to $u_t=D u_{xx}+f(x,t)$, or the <transport equation> to $u_t+c u_x=f(x,t)$. If $u$ is a <temperature>, $f$ has units of temperature per time. The formulas below assume $f=0$; a nonzero <PDE source term> can change the spatial average even with <periodic boundary conditions>.