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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 1-9.doi: 10.6040/j.issn.1671-9352.0.2020.687

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一类拟线性瞬态抛物方程组的空间二择性

李远飞,李丹丹,陈雪姣,石金诚   

  1. 广东财经大学华商学院数据科学学院, 广东 广州 511300
  • 发布日期:2021-06-03
  • 作者简介:李远飞(1982— ),男,博士,教授,研究方向为偏微分方程. E-mail:liqfd@163.com
  • 基金资助:
    广东省普通高校人文社科类创新团队项目(2020WCXTD008)

Alternative results of a class of quasilinear transient parabolic equations

LI Yuan-fei, LI Dan-dan, CHEN Xue-jiao, SHI Jin-cheng   

  1. School of Data Science, Huashang College Guangdong University of Finance &
    Economics, Guangzhou 511300, Guangdong, China
  • Published:2021-06-03

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摘要： 考虑了在柱体的侧面上满足非线性动力条件的拟线性抛物系统解的空间Phragmén-Lindelöf型二择性。利用微分不等式技术,证明了解随空间变量或者指数式增长或者指数式衰减。通过设置一个大于0的任意常数,获得了更加精确的衰减率和增长率。最后,把二择一定理进一步推广到了二元混合物中的热量方程之中。

关键词: 抛物方程, Phragmén-Lindelö, f二择一, Young不等式, 非线性动力系统

Abstract: In this paper, the spatial Phragmén-Lindelöf type alternative of solutions for quasilinear parabolic systems satisfying nonlinear dynamic conditions on the side of the cylinder is considered. By using the technique of differential inequality, it is proved that the solution increases exponentially or decays exponentially with spatial variables. By setting an arbitrary positive constant, more accurate decay rate and growth rate are obtained. Finally, the alternative theorem is extended to the heat equation in binary mixtures.

Key words: parabolic equation, Phragmén-Lindelö, f alternative, Young inequality, nonlinear dynamic system

中图分类号: 

  • O175.26
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