Stability for inverse source problems by Carleman estimates

Abstract

In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and can simplify 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.

17 pages

References in corpus (2)

• Inverse coefficient problems for a transport equation by local Carleman estimate
• Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

Cited by in corpus (6)

• Inverse problems for first-order hyperbolic equations with time-dependent coefficients
• Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements
• Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation
• Some Inverse Problems for the Burgers Equation and Related Systems
• Observability inequalities for degenerate transport equations
• A Carleman estimate and an energy method for a first-order symmetric hyperbolic system