Inverse moving point source problem for the wave equation
Hanin Al Jebawy, Abdellatif El Badia, Faouzi Triki
Abstract
Abstract 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 points of the boundary over a finite time interval is sufficient to determine uniquely its trajectory. We also derive a Lipschitz stability estimate for the inversion.
Topics & Concepts
MathematicsLipschitz continuityInverse problemWave equationMathematical analysisInversion (geology)InversePoint sourceBoundary (topology)TrajectoryBoundary value problemGeometryPhysicsStructural basinBiologyAstronomyOpticsPaleontologyNumerical methods in inverse problemsStability and Controllability of Differential EquationsSpectral Theory in Mathematical Physics