Question

Consider the diffusion-decay equation,
du/dt - D(d2u/dx2) + ru = 0; 0 < x < L; t > 0
where r and D are positive constants, satisfying the boundary conditions
u(0; t) = 0 and -D(du/dx)(L; t) = -1, and the initial condition u(x;0) = u0(x).
(a) Find the steady state of this system.
(b) How does the steady state depend upon u0(x)?