Polynomial decay of a variable coefficient wave equation with an acoustic undamped boundary condition

Exponential stabilization of wave equation with acoustic boundary conditions and its application to memory‐type boundary

“…Similarly, we can get the exponential decay of the energy E l . This kind of boundary condition as in (58) has been recently considered in Conrad and Mifdal, 15 where they imposed different boundary condition on y t and got the polynomial decay.…”

“…Here, the corresponding energy functional can be defined as Similarly, we can get the exponential decay of the energy E l . This kind of boundary condition as in () has been recently considered in Conrad and Mifdal, 15 where they imposed different boundary condition on y t and got the polynomial decay.…”

“…Recently, wave equations with acoustic boundary conditions have been studied by many authors. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Compared with previous articles on this subject, the main difference of this article is related with Equations (1) 3 and (2) 3 . In most previous work, for instance, 9,[12][13][14]16,17,19 the memory term of 𝜕 𝜈 u t has not been considered.…”

“…The asymptotic behavior was obtained in Beale 3 (Theorem 2.6). Recently, wave equations with acoustic boundary conditions have been studied by many authors 5–19 …”

Stability for semilinear wave equation of variable coefficients with acoustic boundary conditions and general boundary memory feedback

“…We would like to cite [24], where a variable-coefficient wave equation with acoustic boundary conditions and a time-varying delay in the boundary feedback was studied by Li and Chai. See also [17,26] and references therein. In the all papers mentioned above, Riemannian geometry method was used.…”