Dix, Julio G.2018-11-162018-11-161998-08-28Dix, J. G. (1998). Decay of solutions of a degenerate hyperbolic equation. <i>Electronic Journal of Differential Equations, 1998</i>(21), pp. 1-10.1072-6691https://hdl.handle.net/10877/7800This article studies the asymptotic behavior of solutions to the damped, non-linear wave equation ü + yů - m(∇u²) ∆u = ƒ(x, t), which is known as degenerate if the greatest lower bound for m is zero, and non-degenerate if the greatest lower bound is positive. For the nondegenerate case, it is already known that solutions decay exponentially, but for the degenerate case exponential decay has remained an open question. In an attempt to answer this question, we show that in general solutions can not decay with exponential order, but thatu̇is square integrable on [0, ∞). We extend our results to systems and to related equations.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalDegenerate hyperbolic equationAsymptotic behaviorArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.