Related papers: Quantitative unique continuation for wave operator…
Let $\Omega$ be a Riemannian manifold with boundary. The time-optimal version of the BC-method determines the parameters in the $T$-neigh\-bor\-hood $\Omega^T$ of $\partial\Omega$ from the boundary observations (response operator) $R^{2T}$…
Consider the differential operator H = -(1/m(x))L, where L is the N-dimensional Laplacian, in the weighted Hilbert space of square integrable functions on N-dimensional Euclidean space with weight m(x)dx. Here m(x) is a positive step…
In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman…
We develop a framework for the fifth-order Kadomtsev--Petviashvili equation on $\mathbb{T}_x \times \mathbb{R}_y$ within a mean-zero KP-adapted Sobolev scale. A localized high-order feedback acting on the periodic variable yields a…
We report the results of experimental studies of the short time-long wavelength behavior of collective particle displacements in quasi-one-dimensional and quasi-two-dimensional colloid suspensions. Our results are represented by the…
We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative…
We derive two model-independent results for spacetimes with globally bounded tidal fields. These are operational resolution scales of the local-inertial approximation and tidal dynamics; no spacetime discreteness is implied. Given an…
We prove a local unique continuation result for Schr\''odinger operators with time independent Lipschitz metrics and lower order terms which are Gevrey 2 in time and bounded in space. This implies global unique continuation from any open…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
This paper deals with quantitative spectral stability for compact operators acting on $L^2(X,m)$, where $(X,m)$ is a measure space. Under fairly general assumptions, we provide a characterization of the dominant term of the asymptotic…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schr\"odinger operators having this form allow a new approach to the…
Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral triple of a compact connected spin manifold with a finite…
We investigate trend to equilibrium for the damped wave equation with a confining potential in the Euclidean space. We provide with necessary and sufficient geometric conditions for the energy to decay exponentially uniformly. The proofs…
The spectrum of the Laplace operator in a curved strip of constant width built along an infinite plane curve, subject to three different types of boundary conditions (Dirichlet, Neumann and a combination of these ones, respectively), is…
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a…
We establish a new family of Carleman inequalities for wave operators on cylindrical spacetime domains containing a potential that is critically singular, diverging as an inverse square on all the boundary of the domain. These estimates are…
This work considers two linear operators which yield wave modes that are classified as neutrally stable, yet have responses that grow or decay in time. Previously, King et al. (Phys. Rev. Fluids, 1, 2016, 073604:1-19) and Huber et al. (IMA…
We consider discrete one-dimensional Schr\"odinger operators with quasi-Sturmian potentials. We present a new approach to the trace map dynamical system which is independent of the initial conditions and establish a characterization of the…
We develop a general method to bound the spreading of an entire wavepacket under Schr\"odinger dynamics from above. This method derives upper bounds on time-averaged moments of the position operator from lower bounds on norms of transfer…