&nbsp;Phragmén-Lindelöf Alternative Result of the Forchheimer Equations

CHEN Xue-jiao, LI Yuan-fei

doi:10.13371/j.cnki.chin.q.j.m.2021.04.006

Chinese Quarterly Journal of Mathematics >

2021 , Vol. 36 >Issue 4: 395 - 404

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.04.006

Phragmén-Lindelöf Alternative Result of the Forchheimer Equations

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Department of Apllied Mathematics, Guangzhou Huashang College

CHEN Xue-Jiao (1984-), female, native of Guangzhou, Guangdong, lecturer of Guangzhou Huashang College, engages in partial differential equation; LI Yuan-fei (1982-), male, native of Guangzhou, Guangdong, distinguished professor of Guangzhou Huashang College, engages in partial differential equation.

Received date: 2021-08-25

Online published: 2021-12-30

Supported by

Supported by Innovation Team Project of Humanities and Social Sciences in Colleges and Universities of Guangdong Province (Grant No. 2020WCXTd008);

Research Team Project of Guangzhou Huashang College (Grant No. 2021HSKT01).

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Abstract

This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder. Using the energy estimation method and the differential inequality technology, the differential inequality about the solution is derived. By solving this differential inequality, it is proved that the solutions grow polynomially or decay exponentially with spatial variables.

Key words： Phragmén-Lindel\"{o}f alternative result; The differential inequality technology; Forchheimer equations

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CHEN Xue-jiao, LI Yuan-fei . Phragmén-Lindelöf Alternative Result of the Forchheimer Equations[J]. Chinese Quarterly Journal of Mathematics, 2021 , 36(4) : 395 -404 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.04.006

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