Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator
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- by Shuang Liu, Yuan Lou, Rui Peng and Maolin Zhou PDF
- Proc. Amer. Math. Soc. 147 (2019), 5291-5302 Request permission
Abstract:
We investigate the effect of frequency on the principal eigenvalue of a time-periodic parabolic operator with Dirichlet, Robin, or Neumann boundary conditions. The monotonicity and asymptotic behaviors of the principal eigenvalue with respect to the frequency parameter are established. Our results prove a conjecture raised by Hutson, Michaikow, and Poláčik.References
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Additional Information
- Shuang Liu
- Affiliation: Institute for Mathematical Sciences, Renmin University of China, Beijing 100872, People’s Republic of China
- MR Author ID: 1161282
- ORCID: 0000-0002-7198-0064
- Email: liushuangnqkg@ruc.edu.cn
- Yuan Lou
- Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
- MR Author ID: 356524
- Email: lou@math.ohio-state.edu
- Rui Peng
- Affiliation: School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China
- MR Author ID: 728442
- Email: pengrui_seu@163.com
- Maolin Zhou
- Affiliation: Department of Mathematics, School of Science and Technology, University of New England, Armidale, New South Wales 2341, Australia
- MR Author ID: 1049939
- Email: zhouutokyo@gmail.com
- Received by editor(s): January 13, 2019
- Received by editor(s) in revised form: March 26, 2019
- Published electronically: July 1, 2019
- Additional Notes: The first author was partially supported by the NSFC grant No. 11571364 and the Outstanding Innovative Talents Cultivation Funded Programs 2018 of Renmin University of China.
The second author was partially supported by the NSF grant DMS-1411176.
The third author was partially supported by the National Science Foundation (NSF) of China (grants no. 11671175 and 11571200), the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (grant no. PPZY2015A013), and the Qing Lan Project of Jiangsu Province.
The fourth author was partially supported by the Australian Research Council (grant no. DE170101410). - Communicated by: Wenxian Shen
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5291-5302
- MSC (2010): Primary 35P15; Secondary 35K87, 35B10
- DOI: https://doi.org/10.1090/proc/14653
- MathSciNet review: 4021088