相关论文: An inverse problem for the space-time fractional S…

This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schr\"{o}dinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order…

We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the…

We study an analog of the anisotropic Calder\'on problem for fractional Schr\"odinger operators $(-\Delta_g)^\alpha + V$ with $\alpha \in (0,1)$ on closed Riemannian manifolds of dimensions two and higher. We prove that the knowledge of a…

We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…

We establish that the potential appearing in a fractional Schr\"odinger operator is uniquely determined by an internal spectral data.

We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…

In this paper, we introduce an inverse problem of a Schr\"odinger type variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, for $0<s<1$. We determine the unknown bounded potential $q$ from the exterior partial…

In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the…

This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{1,\infty}(\bar{\mathbb{R}^3_{-}},\R^3)$ and $q \in…

In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…

Motivated by inverse problems with a single passive measurement, we introduce and analyze a new class of inverse spectral problems on closed Riemannian manifolds. Specifically, we establish two general uniqueness results for the recovery of…

We study the inverse boundary problem for a nonlinear magnetic Schr\"odinger operator on a conformally transversally anisotropic Riemannian manifold of dimension $n\ge 3$. Under suitable assumptions on the nonlinearity, we show that the…

\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct…

Given a fixed $\alpha \in (0,1)$, we study the inverse problem of recovering the isometry class of a smooth closed and connected Riemannian manifold $(M,g)$, given the knowledge of a source-to-solution map for the fractional Laplace…

We study inverse boundary problems for the magnetic Schr\"odinger operator with H\"older continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n greater…

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in…

We consider the inverse problems of for the fractional Schr\"odinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal…

The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schr\"odinger-type operators on a half-line from the underlying Weyl-Titchmarsh function.

In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded potential $Q$ from infinitely many…