Publications

My research spans singular perturbation theory, boundary and interior layer analysis, and structure-preserving numerical and learning-based methods for stiff partial differential equations. Recent work and selected earlier publications are listed below. A complete list of publications is available in my curriculum vitae.

Recent Work (2024–present)

Accepted

Singular layer neural network methods for singularly perturbed problems with C.-Y. Jung and J. Kim, book chapter in Multiscale Problems and Singular Perturbations: Recent Advancements in Numerical Analysis and Scientific Machine Learning, accepted.

Singular layer PINN methods for steep reaction-diffusion equations in convex polygonal domains with Y. Hong and C.-Y. Jung, AMS proceedings volume (ed. K. Yamazaki), accepted; to appear in 2027.

Singular-layer PINN methods for Burgers’ equation with T.-Y. Chang, Y. Hong, and C.-Y. Jung, Pure and Applied Functional Analysis, accepted.

Published

Singular layer physics-informed neural network method for convection-dominated boundary layer problems in two dimensions with Y. Hong, C.-Y. Jung, and D. Lee, Journal of Computational and Applied Mathematics 474 (2026), 116918.

The 3D Euler equations with inflow, outflow and vorticity boundary conditions with J. Kelliher and A. Mazzucato, Journal de Mathématiques Pures et Appliquées 193 (2025), 103628.

Singular layer physics informed neural network method for plane parallel flows with T.-Y. Chang, Y. Hong, and C.-Y. Jung, Computers and Mathematics with Applications 166 (2024), 91–105.

Semi-analytic PINN methods for boundary layer problems in a rectangular domain with Y. Hong, C.-Y. Jung, and T. Munkhjin, Journal of Computational and Applied Mathematics 450 (2024), 115989.

A staggered discontinuous Galerkin method for the Stokes problem on rectangular meshes with H.-H. Kim, C.-Y. Jung, and T. B. Nguyen, Computers and Mathematics with Applications 162 (2024), 180–195.

Semi-analytic PINN methods for singularly perturbed boundary value problems with Y. Hong and C.-Y. Jung, Applicable Analysis 103 (2024), no. 14, 2554–2571.

Submitted

Finite volume neural networks for viscous Burgers equations in a rectangular domain with C.-Y. Jung and J. Kim, submitted.

Finite volume neural networks for singular perturbation problems in a rectangular domain with C.-Y. Jung and J. Kim, submitted.

Finite volume neural networks for singularly perturbed boundary value problems with J. Kim, submitted; revised version under review at the International Journal of Numerical Analysis and Modeling.

Physics-informed neural network approach for singular layers in periodic parallel pipe flows with M. Moon, Y. Hong, and C.-Y. Jung, submitted to the Journal of Computational and Applied Mathematics.

Selected Earlier Publications

Singular perturbations and boundary layers with M. Hamouda, C.-Y. Jung, and R. Temam, Springer, 2018.

A reference monograph on singular perturbation problems and boundary layers arising in fluid dynamics and related systems.

Vanishing viscosity limit of some symmetric flows with J. Kelliher, M. Lopes Filho, A. Mazzucato, and H. Nussenzveig Lopes, Annales de l’Institut Henri Poincaré C: Analyse Non Linéaire, 2019.

Provides rigorous analysis of vanishing viscosity limit and boundary layer formation.

Recent progresses in boundary layer theory with C.-Y. Jung and R. Temam, Discrete and Continuous Dynamical Systems, Series A, 2016.

Analyzes geometric effects on asymptotic boundary layer structure.

Enriched Finite Volume approximations of the plane-parallel flow at a small viscosity with C.-Y. Jung and H. Lee, Journal of Scientific Computing, 2020.

Develops structure-preserving hybrid numerical methods for stiff partial differential equations.

Complete List of Publications

A complete and up-to-date list of publications, including preprints and accepted articles, is available in my curriculum vitae.