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' (ut = |u|p-1 u in Ω × (0, T), where p > 1 and j' 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 ©.
Indiana University Mathematics Journal
Barbu, V., Lasiecka, I., & Rammaha, M. (2007). Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms. Indiana University Mathematics Journal, 56 (3), 995-1021. https://doi.org/10.1512/iumj.2007.56.2990