Energy decay of a variable-coefficient wave equation with memory type acoustic boundary conditions
An initial boundary value problem for the homogeneous wave equation with variable coefficients in a bounded domain of \(\mathbb R^n\) modeling the evolution of the sound in a compressible fluid is investigated. A part of the boundary surface is modeled as a non-dissipative portion and on the other part the so called acoustic boundary conditions involving an integral term are introduced. Under usual conditions for the initial data and some special assumptions regarding the entries in the boundary data, the well-posedness of the stated problem is assured. Then, for the solution of this problem the corresponding energy could be defined. The main result of the paper consist in proving an estimation for this energy, the energy decay. For the proof, one makes use of the Riemannian geometry method.
scientific article; zbMATH DE number 6506832
scientific article