Nonlinear wave equation with weak dissipative term in domains with non-locally reacting boundary. (English) Zbl 1360.76311

Vicente, A.; Frota, C. L.

Wave Motion 50, No. 2, 162-169 (2013).

Summary: In this paper we study the existence and uniqueness of the global solution of a mixed problem associated to a Carrier Equation with weak dissipative term in a bounded domain of \(\mathbb R^n\). On a boundary portion of the domain we consider acoustic boundary conditions to a non-locally reacting boundary. The asymptotic behavior of the energy associated to the problem is also studied.

MSC:

76Q05

Hydro- and aero-acoustics

Keywords:

nonlinear wave equation; non-locally reacting boundary; acoustic boundary conditions; Laplace-Beltrami operator