Uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions
This model has been considered by the author in a recent paper [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 18, 6562--6569 (2012; Zbl 1252.35179)]. He proved the existence of a solution. The energy \(E(t)\) of the model is defined here using the Riemannian metric in \(\mathbb R^n\). The energy estimate is proved under some special assumptions on the coefficients of the considered IBV problem, involving a condition related to a certain escape vector field. This type of conditions have been introduced, some times ago, while studying the controllability of the wave equation with variable coefficients.
scientific article; zbMATH DE number 6125391
scientific article