Please solve it. Thank You.

Q7 (7 points) A cylindrical rod with insulated sides of length L has flat ends. The left end is insulated and temperature at the right end is kept constant at 4 C below zero. At time 0, for each point before the midpoint of the rod, temperature is twice the distance from that point to the mid point of the rod; and for each point in the second half of the rod, temperature is half of the distance from that point to the right end of the rod. At each point between the two ends of the rod heat is generated at a rate g(a, b) per unit volume per unit time. Set up but do not solve a boundary value problem for the temperature U (,) assuming that the medium is isotropic and homogeneous. Include the partial differential equation, all boundary and initial conditions, and include intervals on which they must be satisfied. Also identify Dirichlet and Neumann boundary conditions