Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions

Exponential stability of the nonlinear transmission acoustic problem

“…, which proves (19). The initial conditions (20) to (22) can be proven in a standard way, and this completes the proof of the existence of solution.…”

“…The acoustic boundary conditions were introduced by Beale and Rosencrans 8 and studied in previous literatures. [9][10][11][12][13][14][15][16][17][18][19][20] Beale and Rosencrans 8 derived u tt − Δu = 0 in Ω × (0, ∞) , u = t on Γ × (0, ∞) ,…”

Blow‐up of solution of wave equation with internal and boundary source term and non‐porous viscoelastic acoustic boundary conditions

“…After [25] many authors showed decay results of the energy to problems involving memory and acoustic boundary conditions, see [3,4,[15][16][17][18]23,26]. We highlight the work of Boukhatem and Benabderrahmane [4] where was showed blow up of solutions. In all this papers was considered the porous case ( = 0).…”

“…The study involving the interaction between source term and acoustic boundary conditions can be found in [4,10] and [27]. In these papers the authors considered the porous case, i.e., when = 0.…”

Global nonexistence of solutions for a quasilinear wave equation with acoustic boundary conditions

“…2 Department of Mathematics, Pusan National University, Busan, 609-735, South Korea. 3 Institute of Liberal Education, Catholic University of Daegu, Gyeongsan, 712-702, South Korea.…”