Published in Inverse Problems
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving the unknown parameters and some related quantities are obtained, and, second, the unknown parameters have to ...
Published in Computational Mathematics and Mathematical Physics
AbstractFor elliptic equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda {\text{*}}\mathcal{A}\Lambda u + \ell = 0$$\end{document}, we examine...
We consider the so-called ergodic problem for weak solutions of elliptic equations in divergence form, complemented with Neumann boundary conditions. The simplest example reads as the following boundary value problem in a bounded domain of R^N :------−div(A(x)∇u) + λ = H(x, ∇u) in Ω, ------A(x)∇u · n = 0 on ∂Ω,------where A(x) is a coercive matrix ...
Published in Numerical Analysis and Applications
AbstractIn this paper, we discuss a priori error estimates and superconvergence of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$P_0^2$$ \end{document}–\documentclas...
Published in Automation and Remote Control
Linear elliptic equations with the coefficients depending on the control function and its gradient are considered, and an optimal control problem for such equations is studied. The existence and uniqueness of the solution of this problem are proved. The results are applied to the optimal control of the boundary of a given domain.
Published in Lobachevskii Journal of Mathematics
AbstractWe consider a three-dimensional equation of elliptic type with two singular coefficients, for which the Dirichlet problem is studied in a half-cylinder. The study of the problem is carried out using the method of spectral analysis. For the problem posed, using the Fourier method, one-dimensional spectral problems are obtained. Based on the ...
Published in Mathematical Models and Computer Simulations
Abstract—A method is presented for solving interior boundary-value problems for second-order elliptic equations by transition to ray variables. The domain is divided into cells within which the coefficients and sources have the smoothness and continuity properties necessary for the existence of a regular classical solution in the cell. The finite d...
Published in Computational Mathematics and Mathematical Physics
AbstractThe paper is concerned with estimates of the difference between a given function and the exact solution of an elliptic boundary value problem. Estimates of this type have been derived earlier in terms of the natural energy norm. In this work, an approach is proposed to obtain stronger measures of the deviation and relevant estimates applica...
We study global properties of positive radial solutions of −∆u = u p + M ||u| 2p p+1 in R N where p > 1 and M is a real number. We prove the existence or the non-existence of ground states and of solutions with singularity at 0.
A new variant of Incomplete Factorization Implicit (IFI) iterative technique for 2D elliptic finite-difference (FD) equations is suggested which is differed by applying the matrix tridiagonal algorithm. Its iteration parameter is shown be linked with the one for Alternating Direction Implicit method. An effective set of values for the parameter is ...
