Abstract
AbstractThe paper deals with three evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic boundary conditions, but its derivation from the physical model is mathematically not fully satisfactory. The other two models studied in the paper, in the Lagrangian and Eulerian settings, are physically transparent. In the paper the first model is derived from the other two in a rigorous way, also for solutions merely belonging to the natural energy spaces.
Funder
Ministero dell’Università e della Ricerca
Publisher
Springer Science and Business Media LLC
Reference42 articles.
1. R. A. Adams and J. J. F. Fournier, Sobolev spaces, second ed., Pure and Applied Mathematics (Amsterdam), vol. 140, Elsevier/Academic Press, Amsterdam, 2003.
2. A. A. Alcântara, B. A. Carmo, H. R. Clark, R. R. Guardia, and M. A. Rincon, Nonlinear wave equation with Dirichlet and acoustic boundary conditions: theoretical analysis and numerical simulation, Comput. Appl. Math. 41 (2022), no. 4, Paper No. 141, 21.
3. W. Arendt, G. Metafune, D. Pallara, and S. Romanelli, The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions, Semigroup Forum 67 (2003), no. 2, 247–261.
4. W. Arendt and A. F. M. ter Elst, The Dirichlet-to-Neumann operator on$$C(\partial \Omega )$$, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 20 (2020), no. 3, 1169–1196.
5. J. T. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J. 26 (1976), 199–222.