Decay rates for solutions of semilinear wave equations with a memory condition at the boundary

On a semi-linear wave equation associated with memory conditions at the boundaries: unique, existence and regularity

“…What we obtain here is considered as both the generalization and a more effective approach of those in Aassila and Benaissa [1], in Benaddi and Rao [4], Long and Dinh [10], in Phung [19], in Santos [20], in Sengul [21], D. Takači and A. Takači [22] and in mine [16]- [18], [24], [25].…”

“…(1.1), and we shortly call the sum G (u(x, t)) + H ∂u ∂t (x, t) the damping-source term. The problems of wave equations associated with memory conditions or integral equations at the boundaries have interested many mathematicians (see [5], [10]- [20], [22], [24], [25]). …”

“…In [20], Santos studied the asymptotic behavior of the solution of problem (1.1), (1.2), (1.4) in the case of µ(x, t) ≡ µ(t), G(u) = H ∂u ∂t = 0, F (x, t) = 0 associated with a boundary condition of memory type at x = 1 as follows (1.7) u(1, t) +…”

Wave Equation with Acoustic/Memory Boundary Conditions

“…In this direction boundary conditions of memory type, as equation (2), imposed on a portion of the boundary and Dirichlet condition on the rest of the boundary, have been considered, for instance [1], [4], [12] and [13]. Equation (2) means that the portion Γ 0 is clamped in a body with viscoelastic properties.…”

On Nonlinear Coupled System with Nonlocal Boundary Conditions

“…It is worth mentioning some papers in connection with viscoelastic effects on the domain or on the boundary. In this direction we can cite the work by Santos [14] who consider the linear coupled system with memory and proved uniform (exponential and polynomial) decay rates. Also, we can cite the article of Cavalcanti et al [5] where it was considered a linear coupled degenerate system with boundary memory effect.…”