Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping

Asymptotic Behavior of Solutions to Quasilinear Hyperbolic Equations with Nonlinear Damping

Logarithmic decay of hyperbolic equations with arbitrary boundary damping

In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the logarithmic stability estimate for the hyperbolic equations without any assumption on an observation sub-boundary.

On the decay of solutions for a class of quasilinear hyperbolic equations with non-linear damping and source terms

In this paper, we consider the non-linear wave equation utt − ut − div(|∇u|∇u) + a|ut | ut = b|u|u a; b¿0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on , m, and p, we give precise decay rates for the solution. In particular, we show that for m = 0, the decay is exponential. This work improves the result by Yang (Math. Meth. Appl. Sci. 2002; 25:795–814)...

Influence of damping on hyperbolic equations with parabolic degeneracy

This paper examines the effect of damping on a nonstrictly hyperbolic 2×2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line ...

Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition

The asymptotic behavior as well as the global existence of classical solutions to the 3D compressible Euler equations are considered. For polytropic perfect gas P ρ P0ρ , time asymptotically, it has been proved by Pan and Zhao 2009 that linear damping and slip boundary effect make the density satisfying the porous medium equation and the momentum obeying the classical Darcy’s law. In this paper...