8.2.1. Solve the heat equation with time-independent sources and boundary conditions ∂u ∂t = k ∂ 2 u ∂x2 + Q(x) u(x, 0) = f(x) if an equilibrium solution exists. Analyze the limits as t→ [infinity]. If no equilibrium exists, explain why and reduce the problem to one with homogeneous boundary conditions (but do not solve). Assume Haberman, Richard. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, (Pearson Modern Classics for Advanced Mathematics Series) (p. 346). Pearson Education. Kindle Edition.