Question

Heat Equation stationary condition.
My equation is du/dt=a^2 (Laplace oparator)*u+f(M,t) ,f(M,t)-heat energy generated per unit volume per unit time,M=M(x,y,z),u-temepareture.In my problem i have a condition where f=sin(pi/H)x.
So the problem is,when i i have to
v=lim(t->infin.)u(x,t), can i use f=sin(pi/H)x? I doubt it because in stationary problem f normally is constant.