JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 1-9.doi: 10.6040/j.issn.1671-9352.0.2020.687

   

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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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

CLC Number: 

  • O175.26
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