Global wellposedness and exponential stability for Kuznetsov's equation in L_pspaces
Abstract
We investigate a quasilinear initialboundary value problem for Kuznetsov's equation with nonhomogeneous Dirichlet boundary conditions. This is a model in nonlinear acoustics which describes the propagation of sound in fluidic media with applications in medical ultrasound. We prove that there exists a unique global solution which depends continuously on the sufficiently small data and that the solution and its temporal derivatives converge at an exponential rate as time tends to infinity. Compared to the analysis of Kaltenbacher & Lasiecka, we require optimal regularity conditions on the data and give simplified proofs which are based on maximal L_pregularity for parabolic equations and the implicit function theorem.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 arXiv:
 arXiv:1209.1456
 Bibcode:
 2012arXiv1209.1456M
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 35K59 (Primary) 35K51;
 35Q35;
 35B30;
 35B35;
 35B40;
 35B45;
 35B65 (Secondary)
 EPrint:
 14 pages