All Stories

  1. Inner‐Layer Asymptotics in Partially Perforated Domains: Coupling Across Flat and Oscillating Interfaces

    Article • Mathematical Methods in the Applied Sciences, November 2025, Wiley

    Prof. Dr. Taras Mel'nyk

  2. Muskat–Leverett Two‐Phase Flow in Thin Cylindric Porous Media: Asymptotic Approach

    Article • Studies in Applied Mathematics, November 2025, Wiley

    Prof. Dr. Taras Mel'nyk

  3. Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains

    Article • Nonlinear Differential Equations and Applications NoDEA, October 2024, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  4. Asymptotic expansion for convection-dominated transport in a thin graph-like junction

    Article • Analysis and Applications, March 2024, World Scientific Pub Co Pte Lt

    Prof. Dr. Taras Mel'nyk

  5. Spectral problems with perturbed Steklov conditions in thick junctions with branched structure

    Article • Applicable Analysis, March 2024, Taylor & Francis

    Taras Melnyk, Prof. Dr. Taras Mel'nyk

  6. Asymptotic expansions for transport problems in thin graph-like networks

    Article • Asymptotic Analysis, March 2024, IOS Press

    Taras Melnyk, Prof. Dr. Taras Mel'nyk

  7. Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks

    Article • Journal of Mathematical Analysis and Applications, January 2024, Elsevier

    Prof. Dr. Taras Mel'nyk

  8. Complex Analysis

    Article • January 2023, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  9. Asymptotic expansion for the solution of a convection-diffusion problem in a thin graph-like junction

    Article • Asymptotic Analysis, November 2022, IOS Press

    Prof. Dr. Taras Mel'nyk

  10. Asymptotic analysis of spectral problems in thick junctions with the branched fractal structure

    Article • Mathematical Methods in the Applied Sciences, September 2022, Wiley

    Prof. Dr. Taras Mel'nyk

  11. Asymptotic analysis of spectral problems in thick junctions with the branched fractal structure

    Article • May 2022, Wiley

    Prof. Dr. Taras Mel'nyk

  12. Asymptotic approximations for eigenvalues and eigenfunctions of a spectral problem in a thin graph-like junction with a concentrated mass in the node

    Article • Analysis and Applications, December 2020, World Scientific Pub Co Pte Lt

    Prof. Dr. Taras Mel'nyk

  13. Asymptotic analysis of a contact Hele-Shaw problem in a thin domain

    Article • Nonlinear Differential Equations and Applications NoDEA, August 2020, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  14. Homogenization of a nonlinear monotone problem with a big nonlinear Signorini boundary interaction in a domain with highly rough boundary

    Article • Nonlinearity, November 2019, Institute of Physics Publishing

    Prof. Dr. Taras Mel'nyk

  15. Influence of the node on the asymptotic behaviour of the solution to a semilinear parabolic problem in a thin graph-like junction

    Article • Asymptotic Analysis, May 2019, IOS Press

    Arsen Klevtsovskiy, Prof. Dr. Taras Mel'nyk

  16. Asymptotic analysis of a mathematical model of the atherosclerosis development

    Article • International Journal of Biomathematics, February 2019, World Scientific Pub Co Pte Lt

    Prof. Dr. Taras Mel'nyk

  17. Asymptotic Approximations for Solutions to Semilinear Elliptic and Parabolic Problems

    Article • January 2019, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  18. Homogenization of Elliptic Problems in Thick Junctions with Sharp Edges

    Article • January 2019, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  19. Homogenization of Linear Elliptic Problems

    Article • January 2019, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  20. Homogenization of Semilinear Parabolic Problems

    Article • January 2019, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  21. Introduction

    Article • January 2019, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  22. Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2

    Article • January 2019, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  23. Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary

    Article • Journal of Differential Equations, November 2018, Elsevier

    Prof. Dr. Taras Mel'nyk

  24. Asymptotic approximation for semi-linear elliptic problems in thin aneurysm-type domains

    Article • Open Mathematics, November 2017, De Gruyter

    Arsen Klevtsovskiy, Prof. Dr. Taras Mel'nyk

  25. Asymptotic approximation of a nonlinear parabolic problem in a thin star-shaped junction

    Article • Mathematical Methods in the Applied Sciences, November 2017, Wiley

    Arsen Klevtsovskiy, Prof. Dr. Taras Mel'nyk

  26. Erratum to: Asymptotic Approximations of the Solution to a Boundary Value Problem in a Thin Aneurysm Type Domain

    Article • Journal of Mathematical Sciences, September 2017, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  27. Asymptotic Approximations of the Solution to a Boundary Value Problem in a Thin Aneurysm Type Domain

    Article • Journal of Mathematical Sciences, June 2017, Springer Science + Business Media

    Arsen Klevtsovskiy, Prof. Dr. Taras Mel'nyk

  28. Asymptotic expansion for the solution of a problem in a thin cascade domain with a local joint

    Article • Asymptotic Analysis, April 2016, IOS Press

    Arsen Klevtsovskiy, Prof. Dr. Taras Mel'nyk

  29. Homogenization of a semilinear variational inequality in a thick multi-level junction

    Article • Journal of Inequalities and Applications, March 2016, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  30. Eigenvibrations of thick cascade junctions with `very heavy' concentrated masses

    Article • Izvestiya Mathematics, June 2015, Steklov Mathematical Institute

    Prof. Dr. Taras Mel'nyk

  31. Asymptotic approximation for the solution to a semi-linear parabolic problem in a thick junction with the branched structure

    Article • Journal of Mathematical Analysis and Applications, April 2015, Elsevier

    Prof. Dr. Taras Mel'nyk

  32. Asymptotic Approximations for Chemical Reactive Flows in Thick Fractal Junctions

    Article • January 2015, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  33. Asymptotic Expansion of the Solution of an Elliptic Boundary-Value Problem in a Thin Cascade Domain

    Article • Journal of Mathematical Sciences, March 2014, Springer Science + Business Media

    Arsen Klevtsovskiy, Prof. Dr. Taras Mel'nyk

  34. High-frequency cell vibrations and spatial skin effect in thick cascade junction with heavy concentrated masses

    Article • Comptes Rendus Mécanique, February 2014, Cellule MathDoc/CEDRAM

    Prof. Dr. Taras Mel'nyk

  35. Spatial‐skin effect for eigenvibrations of a thick cascade junction with ‘heavy’ concentrated masses

    Article • Mathematical Methods in the Applied Sciences, June 2013, Wiley

    Prof. Dr. Taras Mel'nyk

  36. Homogenization of Boundary Value Problems in Two-Level Thick Junctions Consisting of Thin Disks with Rounded or Sharp Edges

    Article • Journal of Mathematical Sciences, April 2013, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  37. On new types of vibrations of thick cascade junctions with concentrated masses

    Article • Doklady Mathematics, February 2013, Pleiades Publishing Ltd

    Prof. Dr. Taras Mel'nyk

  38. Asymptotic analysis of boundary value and spectral problems in thin perforated regions with rapidly changing thickness and different limiting dimensions

    Article • Sbornik Mathematics, August 2012, Steklov Mathematical Institute

    Prof. Dr. Taras Mel'nyk

  39. Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses

    Article • Applicable Analysis, June 2012, Taylor & Francis

    Prof. Dr. Taras Mel'nyk

  40. Homogenization of a quasilinear parabolic problem with different alternating nonlinear fourier boundary conditions in a two-level thick junction of the type 3:2:2

    Article • Ukrainian Mathematical Journal, May 2012, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  41. Homogenization of a parabolic signorini boundary value problem in a thick plane junction

    Article • Journal of Mathematical Sciences, March 2012, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  42. Asymptotic approximations for solutions to quasilinear and linear elliptic problems with different perturbed boundary conditions in perforated domains

    Article • Asymptotic Analysis, October 2011, SAGE Publications

    Prof. Dr. Taras Mel'nyk

  43. Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

    Article • ESAIM Control Optimisation and Calculus of Variations, August 2011, EDP Sciences

    Prof. Dr. Taras Mel'nyk

  44. Asymptotic approximations for solutions to quasilinear and linear parabolic problems with different perturbed boundary conditions in perforated domains

    Article • Journal of Mathematical Sciences, July 2011, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  45. Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem

    Article • Mathematical Methods in the Applied Sciences, November 2010, Wiley

    Prof. Dr. Taras Mel'nyk

  46. Asymptotic analysis of boundary-value problems in thin perforated domains with rapidly varying thickness

    Article • Neliniini Kolyvannya, November 2010, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  47. Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction

    Article • Russian Journal of Mathematical Physics, March 2010, Pleiades Publishing Ltd

    Prof. Dr. Taras Mel'nyk

  48. Homogenization of elliptic problems with alternating boundary conditions in a thick two-level junction of type 3:2:2

    Article • Journal of Mathematical Sciences, January 2010, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  49. Asymptotic analysis of a parabolic semilinear problem with nonlinear boundary multiphase interactions in a perforated domain

    Article • Journal of Mathematical Sciences, December 2009, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  50. Asymptotic Analysis of an Optimal Control Problem Involving a Thick Two-Level Junction with Alternate Type of Controls

    Article • Journal of Optimization Theory and Applications, October 2009, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  51. Asymptotic approximations of solutions to parabolic boundary value problems in thin perforated domains of rapidly varying thickness

    Article • Journal of Mathematical Sciences, September 2009, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  52. Convergence theorems for solutions and energy functionals of boundary value problems in thick multilevel junctions of a new type with perturbed neumann conditions on the boundary of thin rectangles

    Article • Journal of Mathematical Sciences, May 2009, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  53. Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions

    Article • Sbornik Mathematics, April 2009, Steklov Mathematical Institute

    Prof. Dr. Taras Mel'nyk

  54. Asymptotic analysis of a boundary-value problem with nonlinear multiphase boundary interactions in a perforated domain

    Article • Ukrainian Mathematical Journal, April 2009, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  55. Homogenization of the signorini boundary-value problem in a thick plane junction

    Article • Neliniini Kolyvannya, January 2009, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  56. Homogenization of a boundary value problem in a thick cascade junction

    Article • Journal of Mathematical Sciences, September 2008, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  57. Boundary Homogenization and Reduction of Dimension in a Kirchhoff–Love Plate

    Article • SIAM Journal on Mathematical Analysis, January 2008, Society for Industrial & Applied Mathematics (SIAM)

    Prof. Dr. Taras Mel'nyk

  58. Homogenization of a boundary‐value problem with a nonlinear boundary condition in a thick junction of type 3:2:1

    Article • Mathematical Methods in the Applied Sciences, September 2007, Wiley

    Prof. Dr. Taras Mel'nyk

  59. Homogenization of a boundary value problem with mixed type of boundary conditions in a thick junction

    Article • Differential Equations, May 2007, Pleiades Publishing Ltd

    Prof. Dr. Taras Mel'nyk

  60. Asymptotic approximation for the solution of a boundary-value problem with varying type of boundary conditions in a thick two-level junction

    Article • Neliniini Kolyvannya, July 2006, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  61. Asymptotic behavior of eigenvalues and eigenfunctions of the Fourier problem in a thick multilevel junction

    Article • Ukrainian Mathematical Journal, February 2006, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  62. Asymptotic Approximation of the Solution to the Robin Problem in a Thick Multistructure

    Article • International Journal for Multiscale Computational Engineering, January 2006, Begell House

    Prof. Dr. Taras Mel'nyk

  63. Homogenization of a Boundary-Value Problem with Varying type of Boundary Conditions in a Thick Two-Level Junction

    Article • Neliniini Kolyvannya, April 2005, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  64. Asymptotic Analysis of the Neumann Problem for the Ukawa Equation in a Thick Multi-structure of Type 3:2:2

    Article • January 2005, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  65. Homogenization of the Neumann problem in thick multi‐structures of type 3 : 2 : 2

    Article • Mathematical Methods in the Applied Sciences, December 2004, Wiley

    Prof. Dr. Taras Mel'nyk

  66. Asymptotic analysis of optimal control problems in thick multi-structures

    Article • IFAC Proceedings Volumes, September 2004, Elsevier

    Prof. Dr. Taras Mel'nyk

  67. Integro-Quasidifferential Equations

    Article • Differential Equations, December 2001, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  68. VIBRATIONS OF A THICK PERIODIC JUNCTION WITH CONCENTRATED MASSES

    Article • Mathematical Models and Methods in Applied Sciences, August 2001, World Scientific Pub Co Pte Lt

    Prof. Dr. Taras Mel'nyk

  69. Averaging of Integro-Quasidifferential Equations

    Article • Differential Equations, June 2001, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  70. Homogenization of a contact problem for a system of densely situated punches

    Article • European Journal of Mechanics - A/Solids, January 2001, Elsevier

    Prof. Dr. Taras Mel'nyk

  71. Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1

    Article • Mathematical Methods in the Applied Sciences, March 2000, Wiley

    Prof. Dr. Taras Mel'nyk

  72. On averaging systems with fast and slow variables on an infinite interval

    Article • Siberian Mathematical Journal, November 1999, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  73. Asymptotics of solutions of discontinuous singularly perturbed boundary-value problems

    Article • Ukrainian Mathematical Journal, June 1999, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  74. Decomposition of systems of quasidifferential equations with rapid and slow variables

    Article • Ukrainian Mathematical Journal, March 1999, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  75. Linear singularly perturbed problems with pulse influence

    Article • Ukrainian Mathematical Journal, January 1999, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  76. Averaging of quasidifferential equations with fast and slow variables

    Article • Siberian Mathematical Journal, October 1998, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  77. An iteration method for the problem of averaging in the standard form

    Article • Ukrainian Mathematical Journal, March 1998, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  78. Asymptotic expansions of eigenvalues and eigenfunctions for elliptic boundary-value problems with rapidly oscillating coefficients in a perforated cube

    Article • Journal of Mathematical Sciences, June 1995, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk

  79. Asymptotics of a solution of a discontinuous singularly perturbed Cauchy problem

    Article • Ukrainian Mathematical Journal, November 1994, Springer Science + Business Media

    Prof. Dr. Taras Mel'nyk