Electron. J. Diff. Eqns.,
Vol. 1998(1998), No. 21, pp. 110.
Decay of solutions of a degenerate hyperbolic equation
Julio G. Dix
Abstract:
This article studies the asymptotic behavior of solutions to
the damped, nonlinear wave equation
which is known as degenerate if the greatest lower bound for
is zero, and nondegenerate 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
.
We extend our results to systems and to related equations.
Submitted January 29, 1998. August, 28, 1998.
Math Subject Classification: 35L05, 35B40.
Key Words: Degenerate hyperbolic equation, asymptotic behavior.
Show me the
PDF file (136 KB),
TEX file, and other files for this article.

Julio G. Dix
Department of Mathematics
Texas State University
San Marcos, TX 78666 USA
email: jd01@swt.edu 
Return to the EJDE home page