23 citations · 35 across the 22 of their papers we have counts for
26 papers
Rate of convergence of the -torsion function to the distance function
Farid Bozorgnia, Masoud Bayrami-Aminlouee, Khudoyor Mamayusupov
We prove that the Dirichlet -torsion function converges to the distance to the boundary at the rate in the uniform norm, on every bounded domain and with a co…
Optimal Control in Hilbert Complex Spaces with Finite Element Exterior Calculus
Farid Bozorgnia, Michael Holst, Anshu Kumar +3
We develop a framework for PDE-constrained optimal control on Hilbert complexes and its structure-preserving discretization by finite element exterior calculus (FEEC), with emphasi…
Inverse Robin Spectral Problem for the p-Laplace Operator
Farid Bozorgnia, Olimjon Eshkobilov
We study an inverse Robin spectral problem for the -Laplacian with mixed Dirichlet--Robin boundary conditions. The unknown coefficient lies on an inaccessible Robin portion, and…
Numerical Algorithms for Partially Segregated Elliptic Systems
Farid Bozorgnia, Avetik Arakelyan, Vyacheslav Kungurtsev +1
We develop numerical methods for elliptic systems governed by a ternary partial-segregation constraint, in which three nonnegative components are required to have a vanishing point…
Coincidence criteria and junction obstructions for two partially segregated elliptic systems
Farid Bozorgnia
We compare two singularly perturbed elliptic systems with the same partial-segregation constraint but different limiting mechanisms. System~A is determined by harmonic-difference i…
Gamma Convergence and Smooth Exact-segregation Approximation for Partially Segregated Systems
Farid Bozorgnia, Avetik Arakelyan
We study three-component Dirichlet energies subject to the partial segregation constraint \(u_1u_2u_3=0\). Our main result is a smooth approximation theorem on bounded Lipschitz do…
Optimal Control of Two-Phase Membrane Problem
Farid Bozorgnia, Vyacheslav Kungurtsev
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of t…
Graph Based Semi-supervised Learning Using Spatial Segregation Theory
Farid Bozorgnia, Morteza Fotouhi, Avetik Arakelyan +1
In this work we address graph based semi-supervised learning using the theory of the spatial segregation of competitive systems. First, we define a discrete counterpart over connec…
The regularity with respect to domains of the additive eigenvalues of superquadratic Hamilton--Jacobi equation
Farid Bozorgnia, Dohyun Kwon, Son N. T. Tu
We study the additive eigenvalues on changing domains, along with the associated vanishing discount problems. We consider the convergence of the vanishing discount problem on chang…
Uniqueness of a solution to a general class of discrete system defined on connected graphs
Avetik Arakelyan, Farid Bozorgnia
In this work we prove uniqueness result for an implicit discrete system defined on connected graphs. Our discrete system is motivated from a certain class of spatial segregation of…
A degenerate elliptic-parabolic system arising in competitive contaminant transport
Margarida Baía, Farid Bozorgnia, Léonard Monsaingeon +1
In this work we investigate a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that the…
Numerical approximations of chromatographic models
Farid Bozorgnia, Sonia Seyed Allaei
A numerical scheme based on modified method of characteristics with adjusted advection (MMOCAA) is proposed to approximate the solution of the system liquid chromatography with mul…
The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
Farid Bozorgnia, Leon Bungert, Daniel Tenbrinck
In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigen…
Approximation of the second eigenvalue of the -Laplace operator in symmetric domains
Farid Bozorgnia
A new idea to approximate the second eigenfunction and the second eigenvalue of -Laplace operator is given. In the case of the Dirichlet boundary condition, the scheme has the r…
The first eigenvalue and eigenfunction of a nonlinear elliptic system
Farid Bozorgnia, Seyyed Abbas Mohammadi, Tomas Vejchodsky
In this paper, we study the first eigenvalue of a nonlinear elliptic system involving -Laplacian as the differential operator. The principal eigenvalue of the system and the cor…
Decay estimate for the solution of the evolutionary damped -Laplace equation
Farid Bozorgnia, Peter Lewintan
In this note, we study the asymptotic behavior, as tends to infinity, of the solution to the evolutionary damped -Laplace equation \begin{equation*} u_{tt}+a\, u_t =Δ_p…
A Note on the Paper "Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps"
Allahkaram Shafie, Fari Bozorgnia
In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some…
On a Class of Singularly Perturbed Elliptic Systems with Asymptotic Phase Segregation
Farid Bozorgnia, Martin Burger
This work is devoted to study of a class of elliptic singular perturbed systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study…
Existence Result for Generalized Variational Equality
Allahkaram Shafie, Farid Bozorgnia
In this paper, we prove the existence of a solution to the Stampachia variational inequality under weakened assumptions on the given operator. As a consequence, we provide some suf…
A space-time pseudospectral discretization method for solving diffusion optimal control problems with two-sided fractional derivatives
Mushtaq Salh Ali, Mostafa Shamsi, Hassan Khosravian-Arab +2
We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two ma…
On the Uniqueness of the Solution to a Strongly Competing System
Avetik Arakelyan, Farid Bozorgnia
This work is devoted to prove uniqueness result for the positive solution to a strongly competing system of Lotka - Volterra type in the limiting configuration, when the competitio…
Simplicity of the the first eigenvalue of (p,q) nonlinear elliptic system
Farid Bozorgnia
In this short note, the simplicity of the first eigenvalue of a nonlinear system is shown by an alternative proof; thereby, it states that the first eigenfunctions are unique up to…
A FEM approximation of a two-phase obstacle problem and its a posteriori error estimate
Farid Bozorgnia, Jan Valdman
This paper is concerned with the two--phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify th…
Uniqueness result for long range spatially segregation elliptic system
Farid Bozorgnia
We study a class of elliptic competition-diffusion systems of long range segregation models for two and more competing species. The existence and uniqueness of the solution are sho…