Boundary Value Problems for Parabolic Operators in a Time-Varying Domain

Sungwon Cho; Hongjie Dong; Doyoon Kim

doi:10.1080/03605302.2015.1019628

Boundary Value Problems for Parabolic Operators in a Time-Varying Domain

Sungwon Cho, Hongjie Dong, Doyoon Kim

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

1 Citation (Scopus)

Abstract

We prove the existence of unique solutions to Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is possibly time varying, non-smooth, and satisfies an exterior measure condition.

Original language	English
Pages (from-to)	1282-1313
Number of pages	32
Journal	Communications in Partial Differential Equations
Volume	40
Issue number	7
DOIs	https://doi.org/10.1080/03605302.2015.1019628
Publication status	Published - 2015 Jul 3
Externally published	Yes

Keywords

Blowup low-order coefficients
Exterior measure condition
Parabolic Dirichlet boundary value problems
Time-varying domain
Vanishing mean oscillation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Boundary Value Problems for Parabolic Operators in a Time-Varying Domain",

abstract = "We prove the existence of unique solutions to Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is possibly time varying, non-smooth, and satisfies an exterior measure condition.",

keywords = "Blowup low-order coefficients, Exterior measure condition, Parabolic Dirichlet boundary value problems, Time-varying domain, Vanishing mean oscillation",

author = "Sungwon Cho and Hongjie Dong and Doyoon Kim",

note = "Funding Information: S. Cho was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2012-0003253). H. Dong was partially supported by the NSF under agreement DMS-1056737. D. Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865). Publisher Copyright: {\textcopyright} 2015, Taylor & Francis Group, LLC.",

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doi = "10.1080/03605302.2015.1019628",

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AU - Kim, Doyoon

N1 - Funding Information: S. Cho was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2012-0003253). H. Dong was partially supported by the NSF under agreement DMS-1056737. D. Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865). Publisher Copyright: © 2015, Taylor & Francis Group, LLC.

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AB - We prove the existence of unique solutions to Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is possibly time varying, non-smooth, and satisfies an exterior measure condition.

KW - Blowup low-order coefficients

KW - Exterior measure condition

KW - Parabolic Dirichlet boundary value problems

KW - Time-varying domain

KW - Vanishing mean oscillation

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Boundary Value Problems for Parabolic Operators in a Time-Varying Domain

Abstract

Keywords

ASJC Scopus subject areas

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