EXPONENTIAL STABILITY TO A QUASILINEAR HYPERBOLIC EQUATION WITH INTERNAL DAMPING

Resonance for Quasilinear Hyperbolic Equation

git u) = c(8ft(ii), ? = x dt, where c(£) is a piecewise continuous function and h(u) is a smooth positive function whose first derivative does not change signs. The external effect is assumed to be finite; for simplicity, we suppose also that c(£) has compact support. Our main interest is the behavior of nonlinear waves when the resonance occurs, that is, when the characteristic speed f(u) is c...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Asymptotic Behavior of Solutions to Quasilinear Hyperbolic Equations with Nonlinear Damping

Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms

In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.

Exponential Stability of Wave Equations with Potential and Indefinite Damping

First, we consider the linear wave equation utt−uxx +a(x)ut + b(x)u = 0 on a bounded interval (0, L) ⊂ R. The damping function a is allowed to change its sign. If a := 1 L R L 0 a(x)dx is positive and the spectrum of the operator (∂xx− b) is negative, exponential stability is proved for small ‖a− a‖L2 . Explicit estimates of the decay rate ω are given in terms of a and the biggest eigenvalue of...