Abstract & Overview
A 1-parameter initial boundary value problem for the linear homogeneous degenerate wave equation u tt (t, x; α) -(a(x; α) u x (t, x; α)) x = 0 (JODEA, 28(1), 1 -42) in the space-time rectangle [0, T ]×[-1, +1], where a(x; α) vanishes as |x| α in the subsegment [-c, +c] [-1, +1], x = cx, and α ∈ (0, 2), is considered.The IBVP is splitted into three auxiliary IBVPs, involving two undetermined functions h 1 (t; α) and h 2 (t; α).The auxiliary IBVPs are solved using the method of separation of variables.The matching conditions to gain continuity of the solution u(t, x; α) to the IBVP and its flux are imposed on the solutions u 1 (t, x; α), u 2 (t, x; α), and u 3 (t, x; α) to the auxiliary IBVPs to derive a linear convolution integro-differential system with respect to h 1 (t; α) and h 2 (t; α).