Related papers: Mean value methods for solving the heat equation b…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…
We study the optimal timing strategies for trading a mean-reverting price process with afinite deadline to enter and a separate finite deadline to exit the market. The price process is modeled by a diffusion with an affine drift that…
We consider the space-time boundary element method (BEM) for the heat equation with prescribed initial and Dirichlet data. We propose a residual-type a posteriori error estimator that is a lower bound and, up to weighted $L_2$-norms of the…
In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…
We investigate the Cauchy problem for a class of nonlinear elliptic operators with $C^\infty$-coefficients at a regular set $\Omega \subset R^n$. The Cauchy data are given at a manifold $\Gamma \subset \partial\Omega$ and our goal is to…
In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one…
We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…
In this paper, we carry out in-depth research centering around the Harnack inequality for positive solutions to nonlinear heat equation on Finsler metric measure manifolds with weighted Ricci curvature ${\rm Ric}_{\infty}$ bounded below.…
In this paper, we consider an inverse problem to determine a source term in a parabolic equation, where the data are obtained at a certain time. In general, this problem is ill-posed, therefore the Tikhonov regularization method is proposed…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
The backwards diffusion equation is one of the classical ill-posed inverse problems, related to a wide range of applications, and has been extensively studied over the last 50 years. One of the first methods was that of {\it…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG)…
The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…