Publication Date:
2011-06-06
Description:
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. Content Type Journal Article Pages 1-15 DOI 10.1007/s00245-011-9138-9 Authors Stefan Meyer, Naturwissenschaftliche Fakultät II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany Mathias Wilke, Naturwissenschaftliche Fakultät II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany Journal Applied Mathematics & Optimization Online ISSN 1432-0606 Print ISSN 0095-4616
Print ISSN:
0095-4616
Electronic ISSN:
1432-0606
Topics:
Mathematics
