Related papers: Reconstruction of a convolution kernel in a semili…

We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear…

In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…

We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies…

Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…

In the present article we consider several issues concerning the doubly parabolic Keller-Segel system in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, we analyze the global…

Splitting the exponential-like $\varphi$ functions, which typically appear in exponential integrators, is attractive in many situations since it can dramatically reduce the computational cost of the procedure. However, depending on the…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

In this paper, we study two general classes of optimization algorithms for kernel methods with convex loss function and quadratic norm regularization, and analyze their convergence. The first approach, based on fixed-point iterations, is…

We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…

An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…

The present paper provides a new representation of the solution to the fragmentation equation as a power series in the Banach space of Radon measures endowed with the total variation norm. This representation is used to justify how the…

The key tool of this paper is a new Carleman estimate for an arbitrary parabolic operator of the second order for the case of reversed time data. This estimate works on an arbitrary time interval. On the other hand, the previously known…

We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close…

We propose a global convergent numerical method to reconstruct the initial condition of a nonlinear parabolic equation from the measurement of both Dirichlet and Neumann data on the boundary of a bounded domain. The first step in our method…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…

Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and time. Optimal rates of convergence in the energy norm are…

This paper proposes a simple, accurate, and robust approach to single image nonparametric blind Super-Resolution (SR). This task is formulated as a functional to be minimized with respect to both an intermediate super-resolved image and a…

We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to approximate isolated eigenvalues. It is shown that entries…