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This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
In this article, we prove a uniqueness result for a coefficient inverse problems regarding a wave, a heat or a Schr\"odinger equation set on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the…
In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…
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…
Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…
We consider a strongly damped wave equation on compact manifolds, both with and without boundaries, and formulate the corresponding inverse problems. For closed manifolds, we prove that the metric can be uniquely determined, up to an…
We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…
It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is given. It is proved that there is an…
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and…
In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(\beta,\alpha_0,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely. Here $\alpha_0\in S^2$ is a fixed…
An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horv\'ath and Apagyi [Mod. Phys. Lett. B 22, 2137 (2008)] is examined in various aspects and developed further to (re)construct…
Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…
A standard bilinear $L^2$ Strichartz estimate for the wave equation, which underlies the theory of $X^{s,b}$ spaces of Bourgain and Klainerman-Machedon, asserts (roughly speaking) that if two finite-energy solutions to the wave equation are…
This work studies the direct and inverse fixed energy scattering problem for two-dimensional Schroedinger equation with rather general nonlinear index of refraction. In particular, using the Born approximation we prove that all…
This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…
We consider the problem of recovering a smooth, compactly supported potential on R^3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled…
This is a continuation of the authors' previous work (A. Kirsch, Math. Meth. Appl. Sci., 45 (2022): 5737-5773.) on well-posedness of time-harmonic scattering by locally perturbed periodic curves of Dirichlet kind. The scattering interface…