Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation

Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data are sufficiently small and regular, then there exists a unique global solution with optimal L p -regularity. We show furthermore that the solution converges to zero at an exponential rate as time tends to infinity. Our techniques are based on maximal L p -regularity for abstract quasilinear parabolic equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation

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Publisher
Springer-Verlag
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics; Systems Theory, Control
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9138-9
Publisher site
See Article on Publisher Site

Abstract

We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data are sufficiently small and regular, then there exists a unique global solution with optimal L p -regularity. We show furthermore that the solution converges to zero at an exponential rate as time tends to infinity. Our techniques are based on maximal L p -regularity for abstract quasilinear parabolic equations.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2011

References

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