On weak closure of some diffusion equations
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- by Menglan Liao, Lianzhang Bao and Baisheng Yan
- Proc. Amer. Math. Soc. 147 (2019), 3803-3811
- DOI: https://doi.org/10.1090/proc/14610
- Published electronically: June 10, 2019
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Abstract:
We study the closure of approximating sequences of some diffusion equations under certain weak convergence. A specific description of the closure under weak $H^1$-convergence is given, which reduces to the original equation when the equation is parabolic. However, the closure under strong $L^2$-convergence may be much larger, even for parabolic equations.References
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Bibliographic Information
- Menglan Liao
- Affiliation: School of Mathematics, Jilin University, Changchun, Jilin Province 130012, People’s Republic of China; and Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- MR Author ID: 214970
- Email: liaomen1@msu.edu
- Lianzhang Bao
- Affiliation: School of Mathematics, Jilin University, Changchun, Jilin Province 130012, People’s Republic of China; and School of Mathematical Science, Zhejiang University, Hangzhou, Zhejiang Province 310027, People’s Republic of China
- MR Author ID: 1069528
- Email: lzbao@jlu.edu.cn
- Baisheng Yan
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- MR Author ID: 348214
- Email: yanb@msu.edu
- Received by editor(s): March 15, 2018
- Published electronically: June 10, 2019
- Communicated by: Joachim Krieger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3803-3811
- MSC (2010): Primary 35Q99, 35B35; Secondary 49J45
- DOI: https://doi.org/10.1090/proc/14610
- MathSciNet review: 3993773