Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the influence of damping in hyperbolic equations with parabolic degeneracy

Authors: Katarzyna Saxton and Ralph Saxton
Journal: Quart. Appl. Math. 70 (2012), 171-180
MSC (2010): Primary 35L45, 35L67
DOI: https://doi.org/10.1090/S0033-569X-2011-01247-1
Published electronically: August 29, 2011
MathSciNet review: 2920622
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper examines the effect of damping on a nonstrictly hyperbolic $ 2\times 2$ system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of small solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.

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Additional Information

Katarzyna Saxton
Affiliation: Department of Mathematical Sciences, Loyola University, New Orleans, Louisiana 70118
Email: saxton@loyno.edu

Ralph Saxton
Affiliation: Department of Mathematics, University of New Orleans, New Orleans, Louisiana 70148
Email: rsaxton@uno.edu

DOI: https://doi.org/10.1090/S0033-569X-2011-01247-1
Received by editor(s): September 6, 2010
Published electronically: August 29, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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