Large time decay estimates for the Muskat equation

Decay estimates of solutions to the IBq equation

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

Decay Estimates for the Wave Equation with Potential*

Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations

Abstract. We examine the memorphic continuaiton of the cut-off resolvent Rχ(z) = χ(U(T, 0)− z)χ, χ(x) ∈ C 0 (R), where U(t, s) is the propagator related to the wave equation with non-trapping time-periodic perturbations (potential V (t, x) or a periodically moving obstacle) and T > 0 is the period. Assuming that Rχ(z) has no poles z with |z| ≥ 1, we establish a local energy decay and we obtain ...

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...

Estimates from the discrete-time Lyapunov equation