Sharp regularity estimates for solutions of the wave equation and their traces with prescribed neumann data

Sharp regularity estimates for solutions of the wave equation and their traces with prescribed... In this paper the regularity properties of second-order hyperbolic equations defined over a rectangular domain Θ with boundary Γ under the action of a Neumann boundary forcing term in L 2 (0, T ; H 1/4 (Γ)) are investigated. With this given boundary input, we prove by a cosine operator/functional analytical approach that not only is the solution of the wave equation and its derivatives continuous in time, with their pointwise values in a basic energy space (in the interior of Ω), but also that a trace regularity thereof can be assigned for the solution’s time derivative in an appropriate (negative) Sobolev space. This new-found information on the solution and its traces is crucial in handling a mathematical model derived for a particular fluid/structure interaction system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Sharp regularity estimates for solutions of the wave equation and their traces with prescribed neumann data

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Publisher
Springer-Verlag
Copyright
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683328
Publisher site
See Article on Publisher Site

Abstract

In this paper the regularity properties of second-order hyperbolic equations defined over a rectangular domain Θ with boundary Γ under the action of a Neumann boundary forcing term in L 2 (0, T ; H 1/4 (Γ)) are investigated. With this given boundary input, we prove by a cosine operator/functional analytical approach that not only is the solution of the wave equation and its derivatives continuous in time, with their pointwise values in a basic energy space (in the interior of Ω), but also that a trace regularity thereof can be assigned for the solution’s time derivative in an appropriate (negative) Sobolev space. This new-found information on the solution and its traces is crucial in handling a mathematical model derived for a particular fluid/structure interaction system.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 1, 1997

References

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