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Applied Mathematics & Optimization

, Volume 64, Issue 2, pp 257–271 | Cite as

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

  • Stefan Meyer
  • Mathias WilkeEmail author
Article

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.

Keywords

Westervelt equation Optimal regularity Quasilinear parabolic system Exponential stability 

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Naturwissenschaftliche Fakultät II, Institut für MathematikMartin-Luther-Universität Halle-WittenbergHalle (Saale)Germany

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