Abstract We revisit the damped wave equation on two-dimensional torus where region does not satisfy geometric control condition. It was shown in [1] that, for sufficiently regular damping, is stale at a rate close to $t^{-1}$. show that if damping vanishes like Hölder function $|x|^{\beta }$, and addition, boundary of locally strictly convex with positive curvature, stable $t^{-1+\frac {2}{2\be...

In the context of wave-like phenomena, Fourier pseudospectral time-domain (PSTD) algorithms are some of the most efficient time-domain numerical methods for engineering applications. One important drawback of these methods is the so-called Gibbs phenomenon. This error can be avoided by using absorbing boundary conditions (ABC) at the end of the simulations. However, there is an important lack o...

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric...

We obtain KSS, Strichartz and certain weighted Strichartz estimates for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metri...

In this paper, we consider a weakly coupled system of wave and damped Klein-Gordon equation with nonlinearities derivative type. We prove blow-up result for the Cauchy problem associated nonnegative compactly supported data by means an iteration argument.

Use is made of Onsager’s hydrodynamic equation to derive the vibration spectrum of the vortex lattice in d-wave superconductor. In particular the rhombic lattice (i.e. the 45 tilted square lattice) is found to be stable for B > Hcr(t). Here Hcr(t) denotes the critical field at which the vortex lattice transition takes place. Typeset using REVTEX 1 Since the discovery of the triangular vortex la...

This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract result, the semigroup generated by the strongly damped wave equation utt −∆ut −∆u + φ(u) = f with critical nonlinearity is considered, whose attractor is sh...

We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global ex...

The eigenfrequencies associated to a damped wave equation are known to belong to a band parallel to the real axis. Under the assumption of periodicity of the geodesic flow we study the asymptotic distribution of the eigenfrequencies in the band. We show that the set of eigenfrequencies exhibits a cluster structure determined by the Morse index of the closed geodesics and the damping coefficient...