Related papers: A new approach to hyperbolic inverse problems II (…

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable…

We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…

The present paper aims at providing a numerical strategy to deal with PDE-constrained optimization problems solved with the adjoint method. It is done through out a unified formulation of the constraint PDE and the adjoint model. The…

This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…

We give a survey of author's results on the inverse hyperbolic problems with time-dependent and time-independent coefficients. We consider the case of hyperbolic equations with Yang-Mills potentials and the case of domains with obstacles.…

We study a second order hyperbolic initial-boundary value partial differential equation with memory, that results in an integro-differential equation with a convolution kernel. The kernel is assumed to be either smooth or no worse than…

We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…

We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point,…

A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.

In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…

We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…

We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…

In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…

In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…

We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.

We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determined by a single measurement of displacement and normal stress…

In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order…

We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and…