caa a22 4500 445842210 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00245-011-9138-9 doi (NATIONALLICENCE)springer-10.1007/s00245-011-9138-9 Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation [Elektronische Daten] [Stefan Meyer, Mathias Wilke] 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. Springer Science+Business Media, LLC, 2011 Westervelt equation nationallicence Optimal regularity nationallicence Quasilinear parabolic system nationallicence Exponential stability nationallicence Meyer Stefan Naturwissenschaftliche Fakultät II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany aut Wilke Mathias Naturwissenschaftliche Fakultät II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany aut Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 257-271 0095-4616 64:2<257 2011 64 245 https://doi.org/10.1007/s00245-011-9138-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9138-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Meyer Stefan Naturwissenschaftliche Fakultät II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany aut NATIONALLICENCE 700 1- Wilke Mathias Naturwissenschaftliche Fakultät II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 257-271 0095-4616 64:2<257 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer