相关论文: An inverse source problem for the heat equation an…
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…
We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be…
The paper considers the integral Volterra equations of the first kind which are related to the inverse boundary-value heat conduction problem. The algorithms have been developed to numerically solve the respective integral equations, which…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
Given a connected compact Riemannian manifold $(M,g)$ without boundary, $\dim M\ge 2$, we consider a space--time fractional diffusion equation with an interior source that is supported on an open subset $V$ of the manifold. The…
We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…
The paper investigates an inverse problem of recovering the internal source from external temperature measurements in photo-thermal effect. The photo-thermal effect actually involves two physical processes: electromagnetic scattering and…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that…
More than ten years ago Ikehata discovered two mathematical methods for the purpose of extracting information about the location and shape of unknown discontinuity embedded in a known background medium from observation data. The methods are…
We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable…
The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…
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…
In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary,…