Inverse problems for real principal type operators
Lauri Oksanen, Mikko Salo, Plamen Stefanov, Günther Uhlmann
Abstract
abstract: We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.
Topics & Concepts
MathematicsOperator (biology)UniquenessMathematical analysisCauchy distributionInverse problemGravitational singularityBoundary value problemType (biology)InversePrincipal partDifferential operatorNonlinear systemLinear mapBoundary (topology)Applied mathematicsPure mathematicsGeometryPhysicsTranscription factorBiologyChemistryBiochemistryQuantum mechanicsRepressorEcologyGeneNumerical methods in inverse problemsAdvanced Mathematical Modeling in EngineeringMathematical Analysis and Transform Methods