On the wave equation with semilinear porous acoustic boundary conditions

Energy decay of variable‐coefficient wave equation with nonlinear acoustic boundary conditions and source term

“…Remark: The well posedness of solution to problem (Equation 1) (Theorem 2.1) can be proved similarly as in the studies of Jameson Graber and Said-Houari, Nicaise et al, and Boukhatem. [19][20][21] We omit it.…”

Uniform stabilization of wave equation with localized damping and acoustic boundary condition

“…The strategy consists in introducing to the equation (1.3) appropriate (dissipative) term involving the trace of the function u . See [18,19,32] where the authors used this strategy with acoustic boundary conditions. We emphasize the work of Graber and Said-Houari [19] where the authors studied the relation damping/source terms.…”

“…See [18,19,32] where the authors used this strategy with acoustic boundary conditions. We emphasize the work of Graber and Said-Houari [19] where the authors studied the relation damping/source terms. c) Internal damping acting over all the domain: this consists in putting damping terms, which are effective in all domain Ω, in the wave equation, as in [12,13,30,31].…”

Uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions

“…Such models have attracted a lot of attention since the 1960s, see, for instance [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein.…”