Related papers: Weakly elliptic damping gives sharp decay

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of…

We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial…

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with…

The damped nonlinear wave equation, also known as the nonlinear telegraph equation, is studied within the framework of semigroups and eigenfunction approximation. The linear semigroup assumes a central role: it is bounded on the domain of…

We study the weakly non-linear development of shear-driven gravity waves, and investigate the mixing properties of the finite amplitude solutions. Calculations to date have been restricted to the linear theory, which predicts that gravity…

We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air…

In this paper we consider a stabilization problem for the abstract-wave equation with delay. We prove an exponential stability result for appropriate damping coefficient. The proof of the main result is based on a frequency-domain approach.

Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision…

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition…

This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin-Voigt type and is distributed around a neighborhood…

An improvement of [18] on the blow-up region and the lifespan estimate of a weakly coupled system of wave equations with damping and mass in the scale-invariant case and with time-derivative nonlinearity is obtained in this article. Indeed,…

Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are…

Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide…

This article presents a new scheme for studying the dynamics of a quintic wave equation with nonlocal weak damping in a 3D smooth bounded domain. As an application, the existence and structure of weak, strong, and exponential attractors for…

We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical…

We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…

We consider in this article the weakly coupled system of wave equations in the \textit{scale-invariant case} and with time-derivative nonlinearities. Under the usual assumption of small initial data, we obtain an improvement of the…

A classical counterexample due to E. De Giorgi, shows that the weak maximum principle does not remain true for general linear elliptic differential systems. After that, there are some efforts to establish the weak maximum principle for…

In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…