6533b861fe1ef96bd12c58cd

RESEARCH PRODUCT

Fixed angle inverse scattering in the presence of a Riemannian metric

Mikko SaloShiqi Ma

subject

Mathematics - Differential GeometryWork (thermodynamics)01 natural sciencesinversio-ongelmatFixed angleMathematics - Analysis of PDEsIncident waveEuclidean geometryFOS: MathematicssirontaUniqueness0101 mathematicsinverse medium problemPhysicsosittaisdifferentiaaliyhtälöt35Q60 35J05 31B10 35R30 78A40Applied Mathematics010102 general mathematicsMathematical analysisCarleman estimatesRiemannian metricsSymmetry (physics)010101 applied mathematicsfixed angle scatteringDifferential Geometry (math.DG)Metric (mathematics)Inverse scattering problemAnalysis of PDEs (math.AP)

description

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption on the metric, we obtain uniqueness and stability results in the inverse scattering problem for a potential with data generated by two incident waves from opposite directions. Further, similar results are given using one measurement provided the potential also satisfies a symmetry assumption. This work extends the results of [23,24] from the Euclidean case to certain Riemannian metrics.

yearjournalcountryeditionlanguage
2020-08-17
https://dx.doi.org/10.48550/arxiv.2008.07329