Related papers: A monotone iterative reconstruction method for an …
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…
We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a…
We deal with a dynamical system \begin{align*} & u_{tt}-\Delta u+qu=0 && {\rm in}\,\,\,\Omega \times (0,T)\\ & u\big|_{t=0}=u_t\big|_{t=0}=0 && {\rm in}\,\,\,\overline \Omega\\ & \partial_\nu u = f && {\rm in}\,\,\,\partial\Omega \times…
We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…
In this paper, we are interested in reiterated periodic homogenization for a family of parabolic problems with nonstandard growth monotone operators leading to Orlicz spaces. The aim of this work is the determination of the global…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
An inverse problem for a nonlinear biharmonic operator is under consideration in the spirit of Isakov (1993) and Johansson-Nurminen-Salo (2023). We prove that a general nonlinear term of the $Q= Q(x,u, \nabla u, \Delta u)$ associated to a…
In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
We prove the equivariant divergence formula for the axiom A flow attractors, which is a recursive formula for perturbation of transfer operators of physical measures along center-unstable manifolds. Hence the linear response acquires an…
This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…
Motivated by the need to develop a general framework for performing statistical inference for discretely observed random rough differential equations, our aim is to construct a geometric $p$-rough path ${\bf X}$ whose response $Y$, when…
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…
In this study, we investigate a mixed problem linked to a second-order parabolic equation, characterized by temporal dependencies and variable~coefficients, and constrained by non-local, non-self-adjoint boundary conditions. By defining…
Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated…
We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…
We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents operations. In this framework, a key role is played by the…