Consider where c, ρ,K0 and α are functions of x, subject to Assume tha...

Consider

where c, ρ,K₀ and α are functions of x, subject to

Assume that the appropriate eigenfunctions are known.

(a) Show that the eigenvalues are positive if α < 0 (see Section 5.2.1).

(b) Solve the initial value problem.

(c) Briefly discuss limt→∞ u(x, t).