In this review, concerning parabolic equations, we give self-contained descriptions on (1)
derivations of Carleman estimates;(2) methods for applications of the Carleman estimates to …

This book summarizes the main analytical and numerical results of Carleman estimates. In
the analytical part, Carleman estimates for three main types of Partial Differential Equations …

Carleman estimates for global uniqueness, stability and numerical methods for coefficient
inverse problems Page 1 J. Inverse Ill-Posed Probl. 21 (2013), 477 – 560 DOI 10.1515/jip-2012-0072 …

In this paper, we study an inverse problem for linear parabolic system with variable diffusion
coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for …

We give a new stability estimate for the problem of determining the time-dependent zero
order coefficient in a parabolic equation from a partial parabolic Dirichlet-to-Neumann map …

The retrospective inverse problem for evolution equations is formulated as the
reconstruction of unknown initial data by a given solution at the final time. We consider the …

We are concerned with an inverse problem of simultaneously recovering the initial value
and source strength in a transmission problem for a parabolic equation from extra …

This article concerns the inverse problem of retrieving a stationary potential for the
Schrödinger evolution equation in a bounded domain of ℝ N with Dirichlet data and …

We study parameter estimation for one-dimensional energy balance models with memory
(EBMMs) given localized and noisy temperature measurements. Our results apply to a wide …

An algorithm has been developed for numerically solving the source determination problem
in the model of information dissemination in synthetic online social networks, described by …