ENERGY DECAY RATES FOR THE KELVIN-VOIGT TYPE WAVE EQUATION WITH ACOUSTIC BOUNDARY

Energy Decay Rate for the Kirchhoff Type Wave Equation with Acoustic Boundary

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with acoustic boundary in a bounded domain in Rn. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations ...

Uniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type

In this article we study the hyperbolic problem (1) where R is a bounded region in Rn whose boundary is partitioned into disjoint sets ro, rl. We prove that the dissipation given by the memory term is strong enough to assure exponential (or polynomial) decay provided the relaxation function also decays exponentially (or polynomially). In both cases the solution decays with the same rate of the ...

Stability of an abstract-wave equation with delay and a Kelvin-Voigt damping

Polynomial decay for the energy with an acoustic boundary condition

In this paper, we establish the polynomial decay for the energy of a wave motion in a bounded domain ~ C II~ 3 with a smooth boundary Oft = F, on a part F0 of which an acoustic boundary condition is subjected. The multiplicative techniques and energy method are used.