Interaction of localized large diffusion and boundary conditions

Aníbal Rodríguez-Bernal; Alejandro Vidal-López

doi:10.1016/j.jde.2019.03.031

Interaction of localized large diffusion and boundary conditions

Aníbal Rodríguez-Bernal^*, Alejandro Vidal-López

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper we derive the limiting PDES for parabolic problems where localized large diffusion touches the boundary of the domain. Hence the limit problem reflects the interaction of large diffusion and boundary conditions. The limit problem is a PDE coupled with a system of ODEs through some nonlocal terms. We study the well posedness and dissipativity of the (nonstandard)limit problem as well as the continuity of the dynamics as diffusion becomes large.

Original language	English
Pages (from-to)	2687-2736
Number of pages	50
Journal	Journal of Differential Equations
Volume	267
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2019.03.031
Publication status	Published - 15 Aug 2019

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Rodríguez-Bernal, A., & Vidal-López, A. (2019). Interaction of localized large diffusion and boundary conditions. Journal of Differential Equations, 267(5), 2687-2736. https://doi.org/10.1016/j.jde.2019.03.031

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title = "Interaction of localized large diffusion and boundary conditions",

abstract = "In this paper we derive the limiting PDES for parabolic problems where localized large diffusion touches the boundary of the domain. Hence the limit problem reflects the interaction of large diffusion and boundary conditions. The limit problem is a PDE coupled with a system of ODEs through some nonlocal terms. We study the well posedness and dissipativity of the (nonstandard)limit problem as well as the continuity of the dynamics as diffusion becomes large.",

author = "An{\'i}bal Rodr{\'i}guez-Bernal and Alejandro Vidal-L{\'o}pez",

note = "Funding Information: Partially supported by ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).Partially supported by Project MTM2016-75465, MICINN and GR58/08 Grupo 920894, UCM, Spain.Partially supported by PRX17/00522 Programa Salvador de Madariaga MECyD, Spain. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = aug,

day = "15",

doi = "10.1016/j.jde.2019.03.031",

language = "English",

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journal = "Journal of Differential Equations",

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T1 - Interaction of localized large diffusion and boundary conditions

AU - Rodríguez-Bernal, Aníbal

AU - Vidal-López, Alejandro

N1 - Funding Information: Partially supported by ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).Partially supported by Project MTM2016-75465, MICINN and GR58/08 Grupo 920894, UCM, Spain.Partially supported by PRX17/00522 Programa Salvador de Madariaga MECyD, Spain. Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/8/15

Y1 - 2019/8/15

N2 - In this paper we derive the limiting PDES for parabolic problems where localized large diffusion touches the boundary of the domain. Hence the limit problem reflects the interaction of large diffusion and boundary conditions. The limit problem is a PDE coupled with a system of ODEs through some nonlocal terms. We study the well posedness and dissipativity of the (nonstandard)limit problem as well as the continuity of the dynamics as diffusion becomes large.

AB - In this paper we derive the limiting PDES for parabolic problems where localized large diffusion touches the boundary of the domain. Hence the limit problem reflects the interaction of large diffusion and boundary conditions. The limit problem is a PDE coupled with a system of ODEs through some nonlocal terms. We study the well posedness and dissipativity of the (nonstandard)limit problem as well as the continuity of the dynamics as diffusion becomes large.

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U2 - 10.1016/j.jde.2019.03.031

DO - 10.1016/j.jde.2019.03.031

M3 - Article

AN - SCOPUS:85063540726

SN - 0022-0396

VL - 267

SP - 2687

EP - 2736

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 5

ER -

Interaction of localized large diffusion and boundary conditions

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