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

• Autorzy: Taras A. Mel’nyk , Arsen V. Klevtsovskiy
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 35J65: Nonlinear boundary value problems for linear elliptic equations
• 74K30: Junctions
• 35B40: Asymptotic behavior of solutions
• 35B25: Singular perturbations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1351-1370

Daty

wydano

2017-01-01

zaakceptowano

2017-10-18

otrzymano

2017-11-01

online

2017-11-22

Twórcy

autor

Taras A. Mel’nyk

• , , ,

autor

Arsen V. Klevtsovskiy

• , , ,

Identyfikatory

DOI

10.1515/math-2017-0114