Related papers: A monotone iterative reconstruction method for an …
The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…
We propose a new monotone finite difference discretization for the variational $p$-Laplace operator, \[ \Delta_p u=\text{div}(|\nabla u|^{p-2}\nabla u), \] and present a convergent numerical scheme for related Dirichlet problems. The…
Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…
This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented…
In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…
Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…
We study an inverse problem involving the unique recovery of several lower order anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the knowledge of the Dirichlet to Neumann map on a part of boundary. The…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…
The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the…
We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…
Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem…
We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…
In this paper we consider the inverse problem of vibro-acoustography, a technique for enhancing ultrasound imaging by making use of nonlinear effects. It amounts to determining two spatially variable coefficients in a system of PDEs…
In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator $A$ and a cocoercive operator $B$. We study the asymptotic behaviour of the trajectories generated by a second…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…