Energy decay estimates for a wave equation with nonlinear boundary feedback

Energy Decay Estimates for Lienard’s Equation with Quadratic Viscous Feedback

This article concerns the stabilization for a well-known Lienard’s system of ordinary differential equations modelling oscillatory phenomena. It is known that such a system is asymptotically stable when a linear viscous (motion-activated) damping with constant gain is engaged. However, in many applications it seems more realistic that the aforementioned gain is not constant and does depend on t...

Decay Estimates for the Wave Equation with Potential*

Global Existence and Decay Estimates for Nonlinear Kirchhoff–type Equation with Boundary Dissipation

In this paper, we consider the initial-boundary value problem for nonlinear Kirchhofftype equation utt −φ(‖∇u‖2)Δu−aΔut = b|u|β−2u, where a,b > 0 and β > 2 are constants, φ is a C1 -function such that φ(s) λ0 > 0 for all s 0 . Under suitable conditions on the initial data, we show the existence and uniqueness of global solution by means of the Galerkin method and the uniform decay rate of the e...

Weighted energy decay for 3D wave equation

We obtain a dispersive long-time decay in weighted energy norms for solutions to the 1D wave equation with generic potential. The decay extends the results obtained by Murata for the 1D Schrödinger equation.

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 ...