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O. Ladyženskaja (1968)
Linear and Quasilinear Equations of Parabolic Type, 23
H. Komatsu (1993)
Functional Analysis and Related Topics, 1991
B. Kaltenbacher, I. Lasiecka (2009)
Global existence and exponential decay rates for the Westervelt equationDiscrete and Continuous Dynamical Systems - Series S, 2
R. Denk, Matthias Hieber, J. Prüss (2007)
Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous dataMathematische Zeitschrift, 257
P. Grisvard (1969)
Équations différentielles abstraitesAnnales Scientifiques De L Ecole Normale Superieure, 2
M. Kaltenbacher (2004)
Numerical Simulation of Mechatronic Sensors and Actuators
P. Kunstmann, L. Weis (2004)
Maximal Lp-regularity for Parabolic Equations, Fourier Multiplier Theorems and $H^\infty$-functional Calculus
G. Prato, P. Kunstmann, L. Weis, I. Lasiecka, A. Lunardi, R. Schnaubelt, M. Iannelli, R. Nagel, Susanna Piazzera (2004)
Functional Analytic Methods for Evolution Equations
Hieber Matthias, Pruss Jan (1997)
Heat kernels and maximal lp—lqestimates for parabolic evolution equationsCommunications in Partial Differential Equations, 22
B. Kaltenbacher (2010)
Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior DampingApplied Mathematics & Optimization, 62
(2008)
Technische Akustik: Grundlagen und Anwendungen
M.F. Hamilton, D.T. Blackstock (1998)
Nonlinear Acoustics
Christian Clason, B. Kaltenbacher, S. Veljović (2009)
Boundary optimal control of the Westervelt and the Kuznetsov equationsJournal of Mathematical Analysis and Applications, 356
R. Denk, Matthias Hieber, F. Bertola, C. Kharif (2003)
Fourier multipliers and problems of elliptic and parabolic type
Saale) e-mail: stefan.meyer@mathematik.uni-halle
P. Grisvard (1969)
Équations différentielles abstraitesAnn. Sci. École Norm. Sup., 2
(1968)
Ural’tseva. Linear and quasilinear equations of parabolic type. Translated from the Russian by S. Smith. Translations of Mathematical Monographs
H. Amann (1995)
Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory
G. Burton (2013)
Sobolev Spaces
H. Triebel (1983)
Theory Of Function Spaces
Maximal Lp-RegularityLet (2002)
Maximal Regularity for Evolution Equations in L P -spaces
R. Denk, M. Hieber, J. Prüss (2003)
$\mathcal{R}$ -boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type
G. Dore (1993)
Lp regularity for abstract differential equations
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.
Applied Mathematics and Optimization – Springer Journals
Published: Oct 1, 2011
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