Recovering point sources for the inhomogeneous Helmholtz equation <sup>*</sup>
Gang Bao, Yuantong Liu, Faouzi Triki
Abstract
Abstract 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 knowledge of a single boundary measurement. The main result of the paper is a new Hölder type stability estimate for the inversion under the assumption that the point sources are well separated. The proof of the stability is based on a combination of Carleman estimates and a technique for proving uniqueness of the Cauchy problem.
Topics & Concepts
MathematicsHelmholtz equationUniquenessCauchy distributionInverse problemMathematical analysisStability (learning theory)Point (geometry)Radiative transferHelmholtz free energyType (biology)Point sourceBoundary value problemInversion (geology)InverseBoundary (topology)GeometryPhysicsBiologyEcologyQuantum mechanicsComputer sciencePaleontologyOpticsStructural basinMachine learningNumerical methods in inverse problemsMicrowave Imaging and Scattering AnalysisRadiative Heat Transfer Studies