Please see the attached file for the fully formatted problems.
I accept the possibility that there is a typo in part (c) and that instead it asks you to show that u_t is discontinuous at (0,a/c) instead of u.
Spherical Symmetry, Wave Equations and Continuity are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.