# Avetik Arakelyan's Publications (Full profile)

### Paper

- Uniqueness of a solution to a general class of discrete system defined on connected graphs, Nonlinear Analysis, 239, (2024)
- Graph based semi-supervised learning using spatial segregation theory, Journal of Computational Science, 74, (2023)
- Approximation of the second eigenvalue of the p-Laplace operator in symmetric domains, Journal of Computational and Applied Mathematics, 434, (2023)
- Numerical treatment to a non-local parabolic free boundary problem arising in financial bubbles, Bulletin of the Iranian Mathematical Society, 45, pp. 59-73, (2019)
- Convergence of the finite difference scheme for a general class of the spatial segregation of reaction-diffusion systems, Computers and Mathematics with Applications, 75, (12), pp. 4232-4240, (2018)
- Uniqueness of the Solution to a Strongly Competing System, Electronic Journal of Differential Equations, 2017, (96), pp. 1-8, (2017)
- Two- and Multi-phase Quadrature surfaces, Communications on Pure and Applied Analysis, 16, (6), pp. 2023-2045, (2017)
- A numerical approach for a general class of the spatial segregation of reaction-diffusion systems arising in population dynamics, Computers and Mathematics with Applications, 72, (11), pp. 2823-2838, (2016)
- Multi-phase Quadrature domains and a related minimization problem, Potential Analysis, 45, (1), pp. 135-155, (2016)
- Numerical solution of the Two-phase obstacle problem by finite difference method, Armenian Journal of Mathematics, 7, (2), pp. 15-33, (2015)
- A finite difference method for two-phase parabolic obstacle-like problem, Armenian Journal of Mathematics, 7, (1), pp. 32-49, (2015)
- Numerical algorithms for a variational problem of the spatial segregation of reaction-diffusion systems, Applied Mathematics and Computation, 219, (17), pp. 8863-8875 , (2013)
- Finite difference scheme for Two-phase obstacle problem , Reports of NAS of RA, 111, (3), pp. 224-231, (2011)
- An error estimate for the finite difference scheme for one-phase obstacle problem, Journal of Contemporary Mathematical Analysis, 46, pp. 131-141, (2011)

### Patent

- Generating higher-level semantics data for development of visual content, United States Patent, Patent No.: US 11,579,849 B2, (2023)

### Conference Paper

- A general class of finite difference schemes arising in numerical analysis of Reaction-diffusion systems, Russian-Armenian workshop on mathematical physics, complex analysis and related topics, (2018)
- On a general class of finite difference schemes arising in Reaction-diffusion systems, Conference Dedicated to the Memory of Sergey Mergelyan, pp. 17, (2018)
- Finite difference scheme for a general class of the spatial segregation of reaction-diffusion systems with two population densities, Vestnik kazanskogo gosudarstvennogo energeticheskogo universiteta, (3), pp. 28-35, (2017)
- Two- and Multi-phase Quadrature domains, Stochastic and Analytic Methods in Mathematical Physics, pp. 12, (2016)
- Numerical approximation for a variational problem of the spatial segregation of Reaction-diffusion system, Mathematics in Armenia: Advances and Perspectives, pp. 62, (2013)
- Finite Difference Scheme for Two-Phase Obstacle Problem, Harmonic Analysis and Approximations, V, pp. 22, (2011)
- Finite Difference Scheme for Two-Phase Obstacle Problem, Dynamic systems, nonlinear analysis and their applications, pp. 9-11, (2011)

### Preprint

- On convergence of numerical algorithm of a class of the spatial segregation of reaction-diffusion system with two population densities, pp. 1-14, (2016)