26 citations · 73 across the 11 of their papers we have counts for
11 papers
Asymptotic expansion for the solution of a convection-diffusion problem in a thin graph-like junction
Taras A. Mel'nyk, Arsen V. Klevtsovskiy
A steady-state convection-diffusion problem with a small diffusion of order is considered in a thin three-dimensional graph-like junction consisting of t…
Asymptotic analysis of a contact Hele-Shaw problem in a thin domain
Taras Mel'nyk, Nataliya Vasylyeva
We analyze the contact Hele-Shaw problem with zero surface tension of a free boundary in a thin domain Under suitable conditions on the given data, the one-va…
Asymptotic approximations for eigenvalues and eigenfunctions of a spectral problem in a thin graph-like junction with a concentrated mass in the node
Taras A. Mel'nyk
A spectral problem is considered in a thin graph-like junction that consists of three thin curvilinear cylinders that are joined through a domain (node) of the diameter $\math…
A mathematical model of the atherosclerosis development in thin blood vessels and its asymptotic approximation
Taras A. Mel'nyk
Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles o…
Asymptotic approximation for the solution to a semi-linear parabolic problem in a thin star-shaped junction
Arsen V. Klevtsovskiy, Taras A. Mel'nyk
A semi-linear parabolic problem is considered in a thin star-shaped junction that consists of several thin curvilinear cylinders that are joined through a domain (node) of dia…
Asymptotic approximations of the solution to a boundary-value problem in a thin aneurysm-type domain
A. V. Klevtsovskiy, T. A. Mel'nyk
A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin aneurysm-type domain that consists of thin curvilinear cylinders that are joined t…