Related papers: Inverse problems for quasi-linear elliptic systems…

This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…

This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…

We study the convergence to equilibrium of a class of nonlinear recombination models. In analogy with Boltzmann's H theorem from kinetic theory, and in contrast with previous analysis of these models, convergence is measured in terms of…

We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeatedly solve its linearization by using the quasi-reversibility…

This paper establishes uniqueness results of inverse elastic scattering problem with phaseless near-field data in periodic structures in $\mathbb{R}^2$ and periodic/biperiodic structures in $\mathbb{R}^3$. We use a superposition of two…

We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the "reduced dimensional…

We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…

We study two inverse problems on a globally hyperbolic Lorentzian manifold $(M,g)$. The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood $V\subset M$ of a time-like geodesic $\mu$. Under natural…

In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…

We propose a nonlinear $\sigma$-model in a curved space as a general integrable elliptic model. We construct its exact solutions and obtain energy estimates near the critical point. We consider the Pohlmeyer transformation in Euclidean…

This paper is concerned with model order reduction of parametric Partial Differential Equations (PDEs) using tree-based library approximations. Classical approaches are formulated for PDEs on Hilbert spaces and involve one single linear…

We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying…

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by…

We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…

We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…

This paper presents an integrated framework to construct local-energy solutions to fairly general nonlinear diffusion equations for initial data growing at infinity under suitable assumptions on local-energy estimates for approximate…

We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…

Electrochemical phenomena in biology often unfold in confined geometries where micrometer- to millimeter-scale domains coexist with nanometer-scale interfacial diffuse charge layers. We analyze a model lipid membrane-electrolyte system…