In this book, focusing on hyperbolic systems, we give self-contained descriptions of•
derivations of Carleman estimates;• methods for application of 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 consider an initial/boundary value problem for a fractional diffusion
equation in a bounded domain Ω: $\partial _t^{\alpha} u=\Delta u+ p (x) u $ where $\partial …

This book provides a brief, self-contained introduction to Carleman estimates for three
typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic …

We present a globally convergent numerical algorithm based on global Carleman estimates
to reconstruct the speed of wave propagation in a bounded domain with Dirichlet boundary …

In this paper, we construct a mixture of neural operators (MoNOs) between function spaces
whose complexity is distributed over a network of expert neural operators (NOs), with each …

We consider stability in an inverse problem of determining three spatially varying functions
including the source term and the mass density for a curved plate by the Riemannian …

In this article, we present an inverse problem for the nonlinear 1D Kuramoto–Sivashinsky
(KS) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti …

Let y (h)(t, x) be one solution to\[\partial_t y (t, x)-\sum_ {i, j= 1}^{n}\partial_ {j}(a_
{ij}(x)\partial_i y (t, x))= h (t, x),\thinspace 0< t< T,\thinspace x\in\Omega\] with a non …