Nonlocal problems in perforated domains
In this paper, we analyse nonlocal equations in perforated domains. We consider nonlocal problems of the form with x in a perforated domain. Here J is a nonsingular kernel. We think about as a fixed set ω from where we have removed a subset that we call the holes. We deal both with the Neumann and D...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Cambridge University Press
2019
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 03100caa a22003617a 4500 | ||
|---|---|---|---|
| 001 | PAPER-25825 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205757.0 | ||
| 008 | 190410s2019 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85060610426 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Pereira, M.C. | |
| 245 | 1 | 0 | |a Nonlocal problems in perforated domains |
| 260 | |b Cambridge University Press |c 2019 | ||
| 270 | 1 | 0 | |m Pereira, M.C.; Dpto. de Matemática Aplicada, IME, Universidade de São Paulo, Rua do Matão 1010, Brazil; email: marcone@ime.usp.br |
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a In this paper, we analyse nonlocal equations in perforated domains. We consider nonlocal problems of the form with x in a perforated domain. Here J is a nonsingular kernel. We think about as a fixed set ω from where we have removed a subset that we call the holes. We deal both with the Neumann and Dirichlet conditions in the holes and assume a Dirichlet condition outside ω. In the latter case we impose that u vanishes in the holes but integrate in the whole ℝN (B = ℝN) and in the former we just consider integrals in ℝN minus the holes (B = ℝN ωωϵ). Assuming weak convergence of the holes, specifically, under the assumption that the characteristic function of has a weak limit, weakly∗ in L∞(ω), we analyse the limit as ϵ → 0 of the solutions to the nonlocal problems proving that there is a nonlocal limit problem. In the case in which the holes are periodically removed balls, we obtain that the critical radius is of the order of the size of the typical cell (that gives the period). In addition, in this periodic case, we also study the behaviour of these nonlocal problems when we rescale the kernel in order to approximate local PDE problems. © Royal Society of Edinburgh 2019. |l eng | |
| 536 | |a Article in Press | ||
| 593 | |a Dpto. de Matemática Aplicada, IME, Universidade de São Paulo, Rua do Matão 1010, São Paulo - SP, Brazil | ||
| 593 | |a Dpto. de Matemáticas, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria Pab 1, Buenos Aires, 1428, Argentina | ||
| 690 | 1 | 0 | |a DIRICHLET PROBLEM |
| 690 | 1 | 0 | |a NEUMANN PROBLEM |
| 690 | 1 | 0 | |a NONLOCAL EQUATIONS |
| 690 | 1 | 0 | |a PERFORATED DOMAINS |
| 700 | 1 | |a Rossi, J.D. | |
| 773 | 0 | |d Cambridge University Press, 2019 |p Proc. R. Soc. Edinburgh Sect. A Math. |x 03082105 |t Proceedings of the Royal Society of Edinburgh Section A: Mathematics | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060610426&doi=10.1017%2fprm.2018.130&partnerID=40&md5=42bc33fb28e089fc8d6f7e44c49be571 |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1017/prm.2018.130 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_03082105_v_n_p_Pereira |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v_n_p_Pereira |y Registro en la Biblioteca Digital |
| 961 | |a paper_03082105_v_n_p_Pereira |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 86778 | ||