Related papers: Inverse problems for non-linear hyperbolic equatio…
The topic of this paper is a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space with $3\leq p<5$. We generalize inward/outward energy theory and weighted…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far- or near-field measurement. We show that nonradiating sources having a convex or non-convex corner or edge on their…
This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…
To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…
Under investigation in this work is an extended nonlinear Schr\"{o}dinger equation with nonzero boundary conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation…
This paper is concerned with uniqueness results in inverse acoustic and electromagnetic scattering problems with phaseless total-field data at a fixed frequency. Motivated by our previous work ({\em SIAM J. Appl. Math. \bf78} (2018),…
This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…
This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…
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…