Related papers: Waves, damped wave and observation
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of…
We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the…
We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result, the novelty of…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
We consider the damped wave equation on a compact manifold. We propose different ways of measuring decay of the energy (time averages of lower energy levels, decay for frequency localized data...) and exhibit links with resolvent estimates…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
We propose a numerical method to approximate the exact averaged boundary control of a family of wave equations depending on an unknown parameter sigma. More precisely the control, independent of sigma, that drives an initial data to a…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…
A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…
The theory of controlled mechanical systems of [6, 3, 4] is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and…
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter $\mu_a>0$. We establish observability inequalities for weakly (when…
We suggest the numerical approach to detect eigenfrequencies of trapped modes in waveguides or guided waves in diffraction gratings. At the same time, the approach works perfectly for computation of systems with finitely many scattering…
The semilinear beam equation with impulses, memory and delay is considered. We obtain the approximate controllability. This is done by employing a technique that avoids fixed point theorems and pulling back the control solution to a fixed…
A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…
This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an…