Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms

This article is concerned with the blow-up of generalized solutions to the wave equation utt - Δu + |u|k j\u27 (ut = |u|p-1 u in Ω × (0, T), where p \u3e 1 and j\u27 denotes the derivative of a C1 convex and real valued function j. We prove that every generalized solution to the equation that enjoys an additional regularity blows-up in finite time; whenever the exponent p is greater than the critical value k + m, and the initial energy is negative. Indiana University Mathematics Journal ©