Related papers: Observability estimate for the wave equation with …
This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
We prove estimates for solutions of the Cauchy problem for the inhomogeneous wave equation on $\R^{1+n}$ in a class of Banach spaces whose norms only depend on the size of the space-time Fourier transform. The estimates are local in time,…
We prove observability estimates for oscillatory Cauchy data modulo a small kernel for $n$-dimensional wave equations with space and time dependent $C^2$ and $C^{1,1}$ coefficients using Gaussian beams. We assume the domains and…
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
We consider second-order hyperbolic equations with rough time-independent coefficients. Our main result is that such equations are well posed on the Hardy spaces $\mathcal{H}^{s,1}_{FIO}(\mathbb{R}^{n})$ and…
In the first paper in this series, we introduced "persistent gravitational wave observables" as a framework for generalizing the gravitational wave memory effect. These observables are nonlocal in time and nonzero in the presence of…
The issue of single range based observability analysis and observer design for the kinematics model of a 3D vehicle subject to a constant unknown drift velocity is addressed. The proposed method departs from alternative solutions to the…
In this article, we first prove quantitative estimates associated to the unique continuation theorems for operators with partially analytic coefficients of Tataru, Robbiano-Zuily and H\"ormander. We provide local stability estimates that…
This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…
In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…
Recent results in quantitative homogenisation of the wave equation with rapidly oscillating coefficients are discussed from the operator-theoretic perspective, which views the solution as the result of applying the operator of hyperbolic…
This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a…
In this paper we study a class of variable coefficient third order partial differential operators on $\mathbb{R}^{n+1}$, containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as…
Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic…
We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…
We consider a single copy of a quantum particle moving in a potential and show that it is possible to monitor its complete wave function by only continuously measuring its position. While we assume that the potential is known, no…
For discrete panel data, the dynamic relationship between successive observations is often of interest. We consider a dynamic probit model for short panel data. A problem with estimating the dynamic parameter of interest is that the model…
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we…