2 citations · 8 across the 14 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
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…
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…