6533b861fe1ef96bd12c464b
RESEARCH PRODUCT
RECOVERY OF THE SOUND SPEED FOR THE ACOUSTIC WAVE EQUATION FROM PHASELESS MEASUREMENTS
Joonas IlmavirtaAlden Waterssubject
Mathematics - Differential GeometryHelmholtz equationGeodesicSTABLE DETERMINATIONGeneral Mathematics01 natural sciencesGaussian beamsinversio-ongelmatacoustic wave equationdifferentiaaligeometriaMathematics - Analysis of PDEsSpeed of soundFOS: MathematicsAcoustic wave equationHelmholtz equationphaseless measurements0101 mathematicsosittaisdifferentiaaliyhtälötPhysicsX-ray transformSTABILITYinverse problemsApplied Mathematicsta111010102 general mathematicsMathematical analysisInverse problemX-RAY TRANSFORMWave equation010101 applied mathematicsAmplitudeDifferential Geometry (math.DG)Phase less measurementsAnalysis of PDEs (math.AP)integral geometrydescription
We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the determination of conformal factors. We obtain new stability results for the Hamiltonian flow transform, which allow to recover the higher order terms.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 | Communications in mathematical sciences |