Decay of Solutions of a Degenerate Hyperbolic Equation

Date

1998-08-28

Authors

Dix, Julio G.

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

This article studies the asymptotic behavior of solutions to the damped, non-linear wave equation ü + yů - m(
∇u
<sup>2</sup>) ∆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 that

is square integrable on [0, ∞). We extend our results to systems and to related equations.

Description

Keywords

Degenerate hyperbolic equation, Asymptotic behavior

Citation

Dix, J. G. (1998). Decay of solutions of a degenerate hyperbolic equation. <i>Electronic Journal of Differential Equations, 1998</i>(21), pp. 1-10.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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