11. Superposition Principle for Non-Homogeneous Heat Equation with Non-Homogeneous Boundary Conditions:

: ,

Initial condition:

Boundary conditions: (Dirichlet)

(Neumann)

Supplemental problems: a) steady state solution:

:

b) transient solution:

: ,

The first supplemental problem is a BVP for ODE;

The second supplemental problem is an IBVP problem for a homogeneous Heat Equation with

homogeneous boundary conditions (basic case).

Show that is a solution of the non-homogeneous IBVP.

Solve the problem with , and a) ; b) . Sketch the graph.