Related papers: Spectral asymptotics for the vectorial damped wave…
In this paper, we derive a series of exact analytical closed expressions to calculate the complex eigenfrequencies and the displacement for the corresponding eigenmodes of a viscoelastic (nano-)sphere in the presence of linear damping.…
Let $L$ be a linear, closed, densely defined in a Hilbert space operator, not necessarily selfadjoint. Consider the corresponding wave equations &(1) \quad \ddot{w}+ Lw=0, \quad w(0)=0,\quad \dot{w}(0)=f, \quad \dot{w}=\frac{dw}{dt}, \quad…
In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…
In information transfer, the dissipation of a signal may have crucial importance. The feasibility of reconstructing the distorted signal also depends on this. That is why the study of quantized dissipative transversal single particle…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
We consider simulations of a 2-dimensional gas of hard disks in a rectangular container and study the Lyapunov spectrum near the vanishing Lyapunov exponents. To this spectrum are associated ``eigen-directions'', called Lyapunov modes. We…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
We consider a family of open sets $M_\epsilon$ which shrinks with respect to an appropriate parameter $\epsilon$ to a graph. Under the additional assumption that the vertex neighbourhoods are small we show that the appropriately shifted…
We study a nonlocal wave equation with logarithmic damping which is rather weak in the low frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in the whole space and we study…
The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto 'wave attractors'. For small-amplitude internal waves, the…
We consider the damped hyperbolic equation (1) \epsilon u_{tt} + u_t = u_{xx} + F(u), x \in R, t \ge 0, where \epsilon is a positive, not necessarily small parameter. We assume that F(0) = F(1) = 0 and that F is concave on the interval…
The exponential decay rate of the semigroup $S(t)=e^{t\mathbb{A}}$ generated by the abstract damped wave equation $$\ddot u + 2f(A) \dot u +A u=0 $$ is here addressed, where $A$ is a strictly positive operator. The continuous function $f$,…
A p.c.f. fractal with a regular harmonic structure admits an associated Dirichlet form, which is itself associated with a Laplacian. This Laplacian enables us to give an analogue of the damped stochastic wave equation on the fractal. We…
Sloshing eigenvalues are studied for containers with porous baffles extending throughout the constant (possibly infinite) depth. The fluid transmission across the baffles is described by Darcy's law, and so the spectral problem is…
This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate…
We consider the diffraction of time-harmonic plane waves by a periodic structure, governed by the Helmholtz equation. Bound states in the continuum (BICs) are quasi-periodic fields that remain $L^{2}$-bounded over one period and occur at…
The generalized pseudospectral Legendre method is used to carry out accurate calculations of eigenvalues of the spherically confined isotropic harmonic oscillator with impenetrable boundaries. The energy of the confined state is found to be…
In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are…