Energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions

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

“…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.…”

“…[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. In Liu and Chen, 13 they discussed the equation including the memory term for 𝜕 𝜈 u t on Γ 0 , and also with the viscoelastic term Δu t in the domain Ω. Liu and Sun 14 studied the following problem:…”

“…In Liu and Chen, 13 they discussed the equation including the memory term for ∂ ν u t on Γ 0 , and also with the viscoelastic term Δ u t in the domain Ω. Liu and Sun 14 studied the following problem: With the perturbed energy functional technique, they established a general decay result relying on the behavior of both α ( t ) and g ( t ). Motivated by Jeong et al, Liu, Chen, and Sun, 9,13,14 we intend to study the energy decay rate of () with Lyapunov approach in the framework of Riemannian geometry. Then, as an application, we get the exponential stabilization of the wave equations with memory type acoustic boundar...…”

“…With the perturbed energy functional technique, they established a general decay result relying on the behavior of both 𝛼(t) and g(t). Motivated by Jeong et al, Liu, Chen, and Sun, 9,13,14 we intend to study the energy decay rate of (1) with Lyapunov approach in the framework of Riemannian geometry. Then, as an application, we get the exponential stabilization of the wave equations with memory type acoustic boundary conditions on Γ 1 and no damping terms in the domain Ω.…”

A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions

“…Boukhatem and Benabderrahmane [2,3] studied the existence, blow-up, and decay of solutions for viscoelastic wave equations with acoustic boundary conditions. Recently, many authors have treated wave/beam equations with acoustic boundary conditions, see [7,8,10,12,13,15,16] and the references therein. Graber and Haid-Houari [5] studied the blow-up solutions for a nonlinear wave equation with porous acoustic boundary conditions:…”