Simonett, Gieri and Wilke, Mathias (2017) Well-posedness and longtime behavior for the Westervelt equation with absorbing boundary conditions of order zero. JOURNAL OF EVOLUTION EQUATIONS, 17 (1). pp. 551-571. ISSN 1424-3199, 1424-3202
Full text not available from this repository. (Request a copy)Abstract
We investigate the Westervelt equation from nonlinear acoustics, subject to nonlinear absorbing boundary conditions of order zero, which were recently proposed in Kaltenbacher and Shevchenko (Discrete Contin Dyn Syst 1000-1008, 2015), Shevchenko and Kaltenbacher (J Comput Phys 302:200-221, 2015). We apply the concept of maximal regularity of type L-p to prove global well-posedness for small initial data. Moreover, we show that the solutions regularize instantaneously, which means that they are C-infinity with respect to time t as soon as t > 0. Finally, we show that each equilibrium is stable and each solution which starts sufficiently close to an equilibrium converges at an exponential rate to a possibly different equilibrium.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPACES; |
| Subjects: | 500 Science > 510 Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:00 |
| Last Modified: | 14 Feb 2019 14:32 |
| URI: | https://pred.uni-regensburg.de/id/eprint/273 |
Actions (login required)
 |
View Item |
