Lipschitz stability of an inverse source problem for ADMB-KdV equation

Abstract

The paper is concerned with the inverse source problem for an ADMB-KdV equation, which describes the nonlinear waves generated by a long-wave instability in a viscous film flowing down an inclined rigid surface. The inverse problem aims to determine a spatially varying source function from internal observation data on a suitable subdomain and the whole spatial observation data at a time. We first prove a Carleman in- equality for ADMB-KdV equation, and then apply this Carleman inequality to derive Lipschitz stability for this inverse source problem.