Abstract wave equations with acoustic boundary conditions
Abstract
We define an abstract setting to treat wave equations equipped with time-dependent acoustic boundary conditions on bounded domains of ${\bf R}^n$. We prove a well-posedness result and develop a spectral theory which also allows to prove a conjecture proposed in (Gal-Goldstein-Goldstein, J. Evol. Equations 3 (2004), 623-636). Concrete problems are also discussed.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2010
- DOI:
- 10.48550/arXiv.1008.0293
- arXiv:
- arXiv:1008.0293
- Bibcode:
- 2010arXiv1008.0293M
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Mathematics - Functional Analysis;
- 47D05;
- 47H20;
- 35L20
- E-Print:
- 21 pages. A few minor bugs appearing in the journal version have been fixed