Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem

Paolo Musolino; Gennady Mishuris

doi:10.1098/rsta.2022.0159

Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem

Paolo Musolino^*, Gennady Mishuris

^*Awdur cyfatebol y gwaith hwn

Mathemateg

Ca' Foscari University of Venice

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

2 Dyfyniadau (Scopus)

48 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

We study the asymptotic behaviour of solutions of a boundary value problem for the Laplace equation in a perforated domain in Rn, n≥3, with a (nonlinear) Robin boundary condition on the boundary of the small hole. The problem we wish to consider degenerates in three respects: in the limit case, the Robin boundary condition may degenerate into a Neumann boundary condition, the Robin datum may tend to infinity, and the size ϵ of the small hole where we consider the Robin condition collapses to 0. We study how these three singularities interact and affect the asymptotic behaviour as ϵ tends to 0, and we represent the solution and its energy integral in terms of real analytic maps and known functions of the singular perturbation parameters.

Iaith wreiddiol	Saesneg
Rhif yr erthygl	20220159
Nifer y tudalennau	18
Cyfnodolyn	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Cyfrol	380
Rhif cyhoeddi	2236
Dyddiad ar-lein cynnar	26 Medi 2022
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1098/rsta.2022.0159
Statws	Cyhoeddwyd - 14 Tach 2022

Mynediad at Ddogfen

10.1098/rsta.2022.0159Trwydded: CC BY

ArticleFersiwn derfynol wedi’i chyhoeddi, 448 KBTrwydded: CC BY

Cysylltiad parhaol

Dolen barhaus

Ffeiliau eraill a chysylltiadau

Dolen i’r cyhoeddiad yn Scopus

1 Wedi Gorffen
1 Wrthi'n gweithredu

EffectFact: Effective Factorisation techniques for matrix-functions: Developing theory, numerical methods and impactful applications
Mishuris, G. (Prif Ymchwilydd)
Horizon 2020 -European Commission
01 Medi 2021 → 31 Awst 2025
Prosiect: Ymchwil a ariannwyd yn allanol
Ser Cymru IFA - Development of the tip element to account for singular physical fields near the crack tip and various propagation regimes.
Mishuris, G. (Prif Ymchwilydd)
WEFO
01 Gorff 2020 → 30 Meh 2021
Prosiect: Ymchwil a ariannwyd yn allanol

Dyfynnu hyn

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title = "Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem",

abstract = "We study the asymptotic behaviour of solutions of a boundary value problem for the Laplace equation in a perforated domain in Rn, n≥3, with a (nonlinear) Robin boundary condition on the boundary of the small hole. The problem we wish to consider degenerates in three respects: in the limit case, the Robin boundary condition may degenerate into a Neumann boundary condition, the Robin datum may tend to infinity, and the size ϵ of the small hole where we consider the Robin condition collapses to 0. We study how these three singularities interact and affect the asymptotic behaviour as ϵ tends to 0, and we represent the solution and its energy integral in terms of real analytic maps and known functions of the singular perturbation parameters.",

keywords = "ARTICLES, Research articles, singularly perturbed boundary value problem, Laplace equation, nonlinear Robin condition, perforated domain, integral equations",

author = "Paolo Musolino and Gennady Mishuris",

note = "Funding Information: The authors acknowledge support from the EU through the H2020-MSCA-RISE-2020 project EffectFact, grant agreement ID 101008140. P.M. also acknowledges the support of the grant {\textquoteleft}Challenges in Asymptotic and Shape Analysis - CASA{\textquoteright} from the Ca{\textquoteright} Foscari University of Venice. G.M. also acknowledges support from Ser Cymru Future Generation Industrial Fellowship no. AU224 – 80761. Acknowledgements Publisher Copyright: {\textcopyright} 2022 The Authors.",

year = "2022",

month = nov,

day = "14",

doi = "10.1098/rsta.2022.0159",

language = "English",

volume = "380",

journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "1364-503X",

publisher = "Royal Society",

number = "2236",

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TY - JOUR

T1 - Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem

AU - Musolino, Paolo

AU - Mishuris, Gennady

N1 - Funding Information: The authors acknowledge support from the EU through the H2020-MSCA-RISE-2020 project EffectFact, grant agreement ID 101008140. P.M. also acknowledges the support of the grant ‘Challenges in Asymptotic and Shape Analysis - CASA’ from the Ca’ Foscari University of Venice. G.M. also acknowledges support from Ser Cymru Future Generation Industrial Fellowship no. AU224 – 80761. Acknowledgements Publisher Copyright: © 2022 The Authors.

PY - 2022/11/14

Y1 - 2022/11/14

N2 - We study the asymptotic behaviour of solutions of a boundary value problem for the Laplace equation in a perforated domain in Rn, n≥3, with a (nonlinear) Robin boundary condition on the boundary of the small hole. The problem we wish to consider degenerates in three respects: in the limit case, the Robin boundary condition may degenerate into a Neumann boundary condition, the Robin datum may tend to infinity, and the size ϵ of the small hole where we consider the Robin condition collapses to 0. We study how these three singularities interact and affect the asymptotic behaviour as ϵ tends to 0, and we represent the solution and its energy integral in terms of real analytic maps and known functions of the singular perturbation parameters.

AB - We study the asymptotic behaviour of solutions of a boundary value problem for the Laplace equation in a perforated domain in Rn, n≥3, with a (nonlinear) Robin boundary condition on the boundary of the small hole. The problem we wish to consider degenerates in three respects: in the limit case, the Robin boundary condition may degenerate into a Neumann boundary condition, the Robin datum may tend to infinity, and the size ϵ of the small hole where we consider the Robin condition collapses to 0. We study how these three singularities interact and affect the asymptotic behaviour as ϵ tends to 0, and we represent the solution and its energy integral in terms of real analytic maps and known functions of the singular perturbation parameters.

KW - ARTICLES

KW - Research articles

KW - singularly perturbed boundary value problem

KW - Laplace equation

KW - nonlinear Robin condition

KW - perforated domain

KW - integral equations

UR - http://www.scopus.com/inward/record.url?scp=85138514332&partnerID=8YFLogxK

U2 - 10.1098/rsta.2022.0159

DO - 10.1098/rsta.2022.0159

M3 - Article

C2 - 36154481

SN - 1364-503X

VL - 380

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2236

M1 - 20220159

ER -

Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem

Crynodeb

Mynediad at Ddogfen

Cysylltiad parhaol

Ffeiliau eraill a chysylltiadau

Ôl bys

Prosiectau

EffectFact: Effective Factorisation techniques for matrix-functions: Developing theory, numerical methods and impactful applications

Ser Cymru IFA - Development of the tip element to account for singular physical fields near the crack tip and various propagation regimes.

Dyfynnu hyn