# Asymptotic approximation for the solution to a semi-linear elliptic problem in a thin aneurysm-type domain

Taras A. Mel’nyk; Arsen V. Klevtsovskiy

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1351-1370
- ISSN: 2391-5455

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topTaras A. Mel’nyk, and Arsen V. Klevtsovskiy. "Asymptotic approximation for the solution to a semi-linear elliptic problem in a thin aneurysm-type domain." Open Mathematics 15.1 (2017): 1351-1370. <http://eudml.org/doc/288321>.

@article{TarasA2017,

abstract = {A semi-linear boundary-value problem with nonlinear Robin boundary conditions is considered in a thin 3D aneurysm-type domain that consists of thin curvilinear cylinders that are joined through an aneurysm of diameter 𝓞(ε). Using the multi-scale analysis, the asymptotic approximation for the solution is constructed and justified as the parameter ε → 0. Namely, we derive the limit problem (ε = 0) in the corresponding graph, define other terms of the asymptotic approximation and prove energetic and uniform pointwise estimates. These estimates allow us to observe the impact of the aneurysm on some properties of the solution.},

author = {Taras A. Mel’nyk, Arsen V. Klevtsovskiy},

journal = {Open Mathematics},

keywords = {Multiscale analysis; Thin aneurysm-type domains; Asymptotic approximation; Semi-linear elliptic problem},

language = {eng},

number = {1},

pages = {1351-1370},

title = {Asymptotic approximation for the solution to a semi-linear elliptic problem in a thin aneurysm-type domain},

url = {http://eudml.org/doc/288321},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Taras A. Mel’nyk

AU - Arsen V. Klevtsovskiy

TI - Asymptotic approximation for the solution to a semi-linear elliptic problem in a thin aneurysm-type domain

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1351

EP - 1370

AB - A semi-linear boundary-value problem with nonlinear Robin boundary conditions is considered in a thin 3D aneurysm-type domain that consists of thin curvilinear cylinders that are joined through an aneurysm of diameter 𝓞(ε). Using the multi-scale analysis, the asymptotic approximation for the solution is constructed and justified as the parameter ε → 0. Namely, we derive the limit problem (ε = 0) in the corresponding graph, define other terms of the asymptotic approximation and prove energetic and uniform pointwise estimates. These estimates allow us to observe the impact of the aneurysm on some properties of the solution.

LA - eng

KW - Multiscale analysis; Thin aneurysm-type domains; Asymptotic approximation; Semi-linear elliptic problem

UR - http://eudml.org/doc/288321

ER -

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