Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 

 

Sharp stability estimates for quasi-autonomous evolution equations of hyperbolic type


Author: Philippe Souplet
Journal: Quart. Appl. Math. 57 (1999), 55-85
MSC: Primary 34G20; Secondary 35L99
DOI: https://doi.org/10.1090/qam/1672175
MathSciNet review: MR1672175
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the energy decay of the difference of two solutions for dissipative evolution problems of the type:

$\displaystyle u'' + Lu + g(u') = h(t), \qquad t \ge 0 ,$

including wave and plate equations and ordinary differential equations. In the general case, when the damping term g behaves like a power of the velocity ú, the energy decreases like a negative power of time, multiplied by a constant depending on the initial energies. We provide estimates on these constants and prove their optimality. In the special case of the ordinary differential equation with periodic forcing, we establish, relying on a controllability-like technique, that the decay is in fact exponential, even under very weak damping.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34G20, 35L99

Retrieve articles in all journals with MSC: 34G20, 35L99


Additional Information

DOI: https://doi.org/10.1090/qam/1672175
Article copyright: © Copyright 1999 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website