IUMJ

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

Authors: Viorel Barbu, Irena Lasiecka and Mohammad A. Rammaha

Issue: Volume 56 (2007), Issue 3, 995-1022

Abstract:

This article is concerned with the blow-up of \textit{generalized} solutions to the wave equation $u_{tt} - \Delta u + |u|^k j'(u_t) = |u|^{p-1} u$ in $\Omega \times (0,T)$, where $p > 1$ and $ j'$ denotes the derivative of a $C^1$ 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.