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dc.contributor.authorDix, Julio G. ( )
dc.identifier.citationDix, J. G. (1998). Decay of solutions of a degenerate hyperbolic equation. Electronic Journal of Differential Equations, 1998(21), pp. 1-10.en_US

This article studies the asymptotic behavior of solutions to the damped, non-linear wave equation

ü + yů - m(||∇u||2) ∆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 ||u̇|| is square integrable on [0, ∞). We extend our results to systems and to related equations.

dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 1998, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectDegenerate hyperbolic equationen_US
dc.subjectAsymptotic behavioren_US
dc.titleDecay of Solutions of a Degenerate Hyperbolic Equationen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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