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In this paper, we consider the wave equation on an n-dimensional simplex with Dirichlet boundary conditions. Our main result is an asymptotic observability identity from any one face of the simplex. The novel aspects of the result are that…

We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…

We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we…

Most derivations of acoustic wave equations involve ensuring that causality is satisfied. Here we explore the consequences of also requiring that the medium should be passive. This is a stricter criterion than causality for a linear system…

In the present paper we prove that the pipe Poiseuille flow of parabolic velocity profile attenuates exponentially in time with respect to three dimensional infinitesimal disturbances at all finite wave numbers and Reynolds numbers for…

This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data…

We consider a degenerate/singular wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a…

We investigate the diffraction of singularities of solutions to the linear elastic equation on manifolds with edge singularities. Such manifolds are modeled on the product of a smooth manifold and a cone over a compact fiber. For the…

We formulate a weakly-nonlinear exit condition for open ends of acoustic waveguides without mean flow; to our knowledge this is the first time an acoustic open end has been analysed outside the linear regime. The resulting admittance…

We study wave scattering by a finite transversal strip in a discrete square-lattice waveguide with Dirichlet boundary conditions imposed on the strip and the waveguide walls. The setting is motivated as a discrete analogue of the classical…

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of…

We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…

We study the propagation of one-dimentional optical beams in a weakly nonlocal medium exhibiting cubic-quintic nonlinearity. A nonlinear equation governing the evolution of the beam intensity in the nonlocal medium is derived thereby which…

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…

We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…

The effect of viscosity and thermal conduction on the acoustics in a shear layer above an impedance wall is investigated numerically and asymptotically by solving the compressible linearised Navier-Stokes equations. It is found that…

Although flow in a circular pipe is stable to infinitesimal perturbations, it can be excited to turbulence by finite perturbations whose minimal amplitude shrinks as R goes to infinity (R = Reynolds number). Laboratory experiments have…

In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to…

The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…

This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…