Related papers: Unique determination of a time-dependent potential…

We first establish the presence of a diffractive front in the fundamental solution of the wave operator with a diract delta intial condition in two dimensional euclidean space caused by the potentials perturbation on the spherical…

In this paper, we study the inverse problem of finding a time-dependent multiplier of the right-hand side of a time-fractional one-dimensional diffusion equation with variables coefficients in the case where the usual Cauchy, homogeneous…

We consider the inverse boundary value problem of the simultaneous determination of the coefficients $\sigma$ and $q$ of the equation $-\mbox{div}(\sigma \nabla u)+qu = 0$ from knowledge of the so-called Neumann-to-Dirichlet map, given…

In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.

The problem of interest in this article is to study the (nonlocal) inverse problem of recovering a potential based on the boundary measurement associated with the fractional Schr\"{o}dinger equation. Let $0<a<1$, and $u$ solves…

We consider the recovery of a potential associated with a semi-linear wave equation on $\mathbb{R}^{n+1}$, $n\geq 1$. We show a H\"older stability estimate for the recovery of an unknown potential $a$ of the wave equation $\square u +a…

We study the problem of recovering a time dependent matrix valued potential on a globally hyperbolic manifold from the knowledge of the source to solution map of a wave equation including a connection 1-form term. We exhibit sufficient…

In this paper we consider an inverse problem for determining time - dependent heat conduction coefficient which vanishes at initial moment as a power $ t^{\beta}. $ The case of strong degeneration ($ \beta \ge1$) is studied. To prove the…

The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…

By minimizing the difference between the left- and the right-hand sides of the many-body time-dependent Schr\"{o}dinger equation with the Slater-determinant wave-function, we derive a non-adiabatic and self-interaction free time-dependent…

In this article, for a time-fractional diffusion-wave equation $\pppa u(x,t) = -Au(x,t)$, $0<t<T$ with fractional order $\alpha \in (1,2)$, we consider the backward problem in time: determine $u(\cdot,t)$, $0<t<T$ by $u(\cdot,T)$ and…

We derive a variational formulation for the scalar wave equation in the second-order formulation on bounded Lipschitz domains and homogeneous initial conditions. We investigate a variational framework in a bounded space-time cylinder $Q$…

Let $D\subset \R^n$, $n\geq 3,$ be a bounded domain with a $C^{\infty}$ boundary $S$, $L=-\nabla^2+q(x)$ be a selfadjoint operator defined in $H=L^2(D)$ by the Neumann boundary condition, $\theta(x,y,\lambda)$ be its spectral function,…

Let $A(\beta,\alpha,k)$ be the scattering amplitude corresponding to a real-valued potential which vanishes outside of a bounded domain $D\subset \R^3$. The unit vector $\alpha$ is the direction of the incident plane wave, the unit vector…

We consider the quantitative uniqueness properties for a parabolic type equation $ u_t-\Delta u = w(x,t) \nabla u + v(x,t) u$, when $v \in L^{p_2}_{t} L^{p_1}_x$ and $w \in L^{q_2}_{t} L^{q_1}_x$, with a suitable range for exponents $p_1$,…

We consider the operator $H:= \partial_t -\Delta+V$ in 2D or 3D waveguide. With an adapted global Carleman estimate with singular weight functions we give a stability result for the time dependent part of the potential for this particular…

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…

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…

Data-driven prediction in quantum mechanics consists in providing an approximative description of the motion of any particles at any given time, from data that have been previously collected for a certain number of particles under the…

We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…