Stably determining time-dependent convection–diffusion coefficients from a partial Dirichlet-to-Neumann map. (16th March 2021)

• Record Type: Journal Article
• Authors: Bellassoued, Mourad; Ben Fraj, Oumaima
• Is Part Of: Inverse problems. Volume 37:Number 4(2021)
• Publication Date: 2021-03-16
• Subjects: inverse problems -- parabolic equation -- Dirichlet-to-Neumann map -- arbitrary boundary data; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abe10d
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study in this paper the inverse problem for the dynamical convection–diffusion equation. More precisely, we set logarithmic stability estimates in the determination of the two time-dependent first-order convection term and the scalar potential appearing in the heat equation. The observations here are taken only on an arbitrary open subset of the boundary and are given by a partial Dirichlet-to-Neumann map. For this end, we will reduce our initial problem into an auxiliary one then we will construct particular solutions and apply a special parabolic Carleman estimate.