Journal of Inverse and Ill-posed Problems | 2019
Inverse source problems for the Korteweg–de Vries–Burgers equation with mixed boundary conditions
Abstract
Abstract In this paper, we prove Lipschitz stability results for the inverse source problem of determining the spatially varying factor in a source term in the Korteweg–de Vries–Burgers (KdVB) equation with mixed boundary conditions. More precisely, the Lipschitz stability property is obtained using observation data on an arbitrary fixed sub-domain over a time interval. Secondly, we show that stability property can also be achieved from boundary measurements. Our proofs relies on Carleman inequalities and the Bukhgeim–Klibanov method.