Stability for inverse source problems by Carleman estimates
X Huang, O Yu Imanuvilov, M Yamamoto
Abstract
Abstract In this article, we provide a modified argument for proving stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method does not require any cut-off procedures and therefore simplifies the existing proofs. We establish the conditional stability for inverse source problems for a hyperbolic equation and a parabolic equation, and our method is widely applicable to various evolution equations.
Topics & Concepts
MathematicsStability (learning theory)Inverse problemInverseMathematical analysisApplied mathematicsArgument (complex analysis)Hyperbolic partial differential equationGeneralized inverseExponential stabilityInverse hyperbolic functionInitial value problemNumerical methods in inverse problemsStability and Controllability of Differential EquationsDifferential Equations and Boundary Problems