2 citations · 8 across the 14 of their papers we have counts for
19 papers
Viscosity Supersolution Barriers to a Non-local Free Boundary Problem
Avetik Arakelyan, Lusine Poghosyan
We study a parabolic obstacle partial integro-differential equation (PIDE) with a dynamically moving bilateral free boundary. This type of problem arises in the mathematical modeli…
The Financial Bubble Model with Lévy Jump Processes
Avetik Arakelyan, Rafayel Barkhudaryan, Vigen Khalatyan +1
In this work we consider an extension of the Berestycki--Monneau--Scheinkman (BMS) model for speculative financial bubbles, in which the investor disagreement process is allowed to…
A Mean-Field Game Model For Large-Scale Attrition in Attacker-Defender Systems
Avetik Arakelyan, Tigran Bakaryan, Davit Alaverdyan +2
This paper proposes a novel Mean-Field Game (MFG) framework for large-scale attacker-defender systems aimed at protecting one or multiple High-Value Units (HVUs). Motivated by clas…
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…
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…
Convergence of Physics-Informed Neural Networks for Fully Nonlinear PDE's
Avetik Arakelyan, Rafayel Barkhudaryan
The present work is focused on exploring convergence of Physics-informed Neural Networks (PINNs) when applied to a specific class of second-order fully nonlinear Partial Differenti…
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…
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…
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…
Numerical treatment to a non-local parabolic free boundary problem arising in financial bubbles
Avetik Arakelyan, Rafayel Barkhudaryan, Henrik Shahgholian +1
In this paper we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterat…
Two- and Multi-phase Quadrature Surfaces
Avetik Arakelyan, Jyotshana V. Prajapat, Henrik Shahgholian
In this paper we shall initiate the study of the two- and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The pro…
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…
Convergence of the finite difference scheme for a general class of the spatial segregation of reaction-diffusion systems
Avetik Arakelyan
In this work we prove convergence of the finite difference scheme for equations of stationary states of a general class of the spatial segregation of reaction-diffusion systems wit…
A Numerical Approach for a General Class of the Spatial Segregation of Reaction-Diffusion Systems Arising in Population Dynamics
Avetik Arakelyan, Rafayel Barkhudaryan
In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with $m\geq 2…
Multi-phase Quadrature domains and a related minimization problem
Avetik Arakelyan, Henrik Shahgholian
In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The w…
Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method
Avetik Arakelyan, Rafayel Barkhudaryan, Michael Poghosyan
In this paper we consider the numerical approximation of the two-phase membrane (obstacle) problem by finite difference method. First, we introduce the notion of viscosity solution…
Convergence Analysis of a Numerical Algorithm for Spatial Segregation of Two Population Densities
Avetik Arakelyan
Over the last few decades, the numerical approximation of spatial segregation equations for reaction-diffusion systems with population densities has gained significant interest…
Numerical Algorithms for a Variational Problem of the Spatial Segregation of Reaction-Diffusion Systems
Avetik Arakelyan, Farid Bozorgnia
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a m…
A Finite Difference Method for Two-Phase Parabolic Obstacle-like Problem
Avetik Arakelyan
In this paper we treat the numerical approximation of the two-phase parabolic obstacle-like problem: \[Δu -u_t=λ^+\cdotχ_{\{u>0\}}-λ^-\cdotχ_{\{u<0\}},\quad (t,x)\in (0,T)\timesΩ,\…