Related papers: Weakly elliptic damping gives sharp decay

We consider the free Klein-Gordon equation with periodic damping. We show on this simple model that if the usual geometric condition holds then the decay of the energy is uniform with respect to the oscillations of the damping, and in…

In this paper, we prove pointwise decay rates for cubic and higher order nonlinear wave equations, including quasilinear wave equations, on asymptotically flat and time-dependent spacetimes. We assume that the solution to the linear…

We consider the Cauchy problem for wave equations with localized damping in ${\bf R}^{2}$. The damping is effective only near spatial infinity. We obtain fast energy decay estimate such that $O(t^{-2}\log t)$ as $t \to \infty$. Unlike the…

Using previously developed method of two-dimensional Laplace transform we obtain the characteristic equations k(\omega) for electromagnetic waves in low-collision fully ionized plasma of a plane geometry. We apply here a new, different from…

In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mass and dissipation terms, in particular, allowing for…

We prove local energy decay for the damped wave equation on R^d. The problem which we consider is given by a long range metric perturbation of the Euclidean Laplacian with a short range absorption index. Under a geometric control assumption…

The Weak Turbulence Theory has been applied to waves in thin elastic plates obeying the F\"oppl-Von K\'arm\'an dynamical equations. Subsequent experiments have shown a strong discrepancy between the theoretical predictions and the…

We analyze the dynamic properties of dissipationless Generalized Langevin Equations in the presence of fluid inertial kernels possessing power-law tails, $k(t) \sim t^{-\kappa}$. While for $\kappa >1$ the dynamics is manifestly non ergodic,…

This paper is devoted to studying a type of logarithmic wave equation in non-cylindrical domains. Firstly, by the penalty method, we prove the existence of weak solutions to such kind of equations. Secondly, different from the dissipative…

Decay rates for the energy of solutions of the damped wave equation on the torus are studied. In particular, damping invariant in one direction and equal to a sum of squares of nonnegative functions with a particular number of derivatives…

Let $K$ be a complete discretely valued field. An extension $L/K$ is "weakly totally ramified" if the residue extension is purely inseparable. We sharpen a result of Ax by showing that any Galois-invariant disk in the algebraic closure of…

We study the Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this problem in the uniformly local spaces is verified based on the…

We consider the wave equation with Kelvin-Voigt damping in a bounded domain. The exponential stability result proposed by Liu and Rao or T\'ebou for that system assumes that the damping is localized in a neighborhood of the whole or a part…

We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…

We prove a weak maximum principle for subsolutions of a degenerate, linear, second order elliptic operator with lower order terms, building on the existence results recently proved by the authors and \c{C}etin, Dal and Zeren.

We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler…

We consider weakly coupled systems of semilinear viscoelastic wave equations with different power source nonlinearities in $\mathbb{R}^n$, $n\geq1$ as follows: \begin{equation*} \left\{\begin{aligned} &u_{tt}-\Delta u+g\ast\Delta…

We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak…

We show global existence backwards from scattering data at infinity for semilinear wave equations satisfying the null condition or the weak null condition. Semilinear terms satisfying the weak null condition appear in many equations in…

The open question, which seems to be also the final part, in terms of studying the Cauchy problem for the weakly coupled system of damped wave equations or reaction-diffusion equations, is so far known as the sharp lifespan estimates in the…