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