Related papers: Operator matrices as generators of cosine operator…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are…
This work is devoted to the effective macroscopic dynamics of a weakly damped stochastic nonlinear wave equation with a random dynamical boundary condition. The white noises are taken into account not only in the model equation defined on a…
In this paper we consider unbounded weighted conditional type operators on the space Lp, we give some conditions under which they are densely defined and we obtain a dense subset of the domain. Also, we get that a WCT operator is continuous…
An apparent paradox is resolved that concerns the existence of time operators which have been derived for the quantum harmonic oscillator. There is an apparent paradox because, although a time operator is canonically conjugate to the…
In this paper, we consider the stabilization of wave equations with moving boundary. First, we show the solution behaviour of wave equation with Neumann boundary conditions, that is, the energy of wave equation with mixed boundary…
Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient…
We survey some known results about operator semigroup generated by operator matrices with diagonal or coupled domain. These abstract results are applied to the characterization of well-/ill-posedness for a class of evolution equations with…
This paper establishes the $L^p$ boundedness of wave operators for linear Schr\"odinger equations in $\mathbb{R}^3$ with time-dependent potentials. The approach to the proof is based on new cancellation lemmas. As a typical application…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
Acoustic and elastic wave equations are routinely used in geophysical and engineering studies to simulate the propagation of waves, with a broad range of applications, including seismology, near surface characterization, non-destructive…
In this note, we discuss the ellipticity of the single layer boundary integral operator for the wave equation in one space dimension. This result not only generalizes the well-known ellipticity of the energetic boundary integral formulation…
In this paper, we give easily verifiable sufficient conditions for two classes of perturbed linear, passive PDE systems to be well-posed, and we provide an energy inequality for the perturbed systems. Our conditions are in terms of…
We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…
This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…
We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…
We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We…
The wave operators $W_\pm(H_1,H_0)$ of two selfadjoint operators $H_0$ and $H_1$ are analyzed at asymptotic spectral values. Sufficient conditions for $\|(W_\pm(H_1,H_0)-P_{1}^\mathrm{ac}P_{0}^\mathrm{ac})f(H_0)\| <\infty$ are given, where…