Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation
Journal Article
·
· Applied Mathematics and Optimization
- Martin-Luther-Universitaet Halle-Wittenberg, Naturwissenschaftliche Fakultaet II, Institut fuer Mathematik (Germany)
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{sub 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{sub p}-regularity for abstract quasilinear parabolic equations.
- OSTI ID:
- 22043876
- Journal Information:
- Applied Mathematics and Optimization, Vol. 64, Issue 2; Other Information: Copyright (c) 2011 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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