Nonlocal problems in thin domains
In this paper we consider nonlocal problems in thin domains. First, we deal with a nonlocal Neumann problem, that is, we study the behavior of the solutions to f(x)=∫Ω1×Ω2Jϵ(x−y)(uϵ(y)−uϵ(x))dy with Jϵ(z)=J(z1,ϵz2) and Ω=Ω1×Ω2⊂RN=RN1×RN2 a bounded domain. We find that there is a limit problem, that...
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Academic Press Inc.
2017
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| LEADER | 05982caa a22005897a 4500 | ||
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| 001 | PAPER-14838 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204526.0 | ||
| 008 | 190410s2017 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85015724640 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a JDEQA | ||
| 100 | 1 | |a Pereira, M.C. | |
| 245 | 1 | 0 | |a Nonlocal problems in thin domains |
| 260 | |b Academic Press Inc. |c 2017 | ||
| 270 | 1 | 0 | |m Rossi, J.D.; Dpto. de Matemáticas, FCEyN, Universidad de Buenos AiresArgentina; email: jrossi@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Raugel, G., Dynamics of Partial Differential Equations on Thin Domains (1995) Lecture Notes in Mathematics, 1609. , Springer-Verlag | ||
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| 520 | 3 | |a In this paper we consider nonlocal problems in thin domains. First, we deal with a nonlocal Neumann problem, that is, we study the behavior of the solutions to f(x)=∫Ω1×Ω2Jϵ(x−y)(uϵ(y)−uϵ(x))dy with Jϵ(z)=J(z1,ϵz2) and Ω=Ω1×Ω2⊂RN=RN1×RN2 a bounded domain. We find that there is a limit problem, that is, we show that uϵ→u0 as ϵ→0 in Ω and this limit function verifies ∫Ω2f(x1,x2)dx2=|Ω2|∫Ω1J(x1−y1,0)(U0(y1)−U0(x1))dy1, with U0(x1)=∫Ω2u0(x1,x2)dx2. In addition, we deal with a double limit when we add to this model a rescale in the kernel with a parameter that controls the size of the support of J. We show that this double limit exhibits some interesting features. We also study a nonlocal Dirichlet problem f(x)=∫RNJϵ(x−y)(uϵ(y)−uϵ(x))dy, x∈Ω, with uϵ(x)≡0, x∈RN∖Ω, and deal with similar issues. In this case the limit as ϵ→0 is u0=0 and the double limit problem commutes and also gives v≡0 at the end. © 2017 Elsevier Inc. |l eng | |
| 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, 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 THIN DOMAINS |
| 700 | 1 | |a Rossi, J.D. | |
| 773 | 0 | |d Academic Press Inc., 2017 |g v. 263 |h pp. 1725-1754 |k n. 3 |p J. Differ. Equ. |x 00220396 |w (AR-BaUEN)CENRE-288 |t Journal of Differential Equations | |
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