JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (12): 1-12.doi: 10.6040/j.issn.1671-9352.0.2020.201

   

Phragmén-Lindelof alternative for the heat conduction equations in a binary mixture

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

  1. School of Data Science, Huashang College Guangdong University of Finance &
    Economics, Guangzhou 511300, Guangdong, China
  • Published:2020-12-01

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Abstract: The heat conduction equations in a binary mixture which are defined in a semi-infinite cylinder is considered and the generatrix of the cylinder is parallel to the coordinate axis. Assuming that the equations satisfy the nonhomogeneous Neumann boundary conditions on the lateral surface of the cylinder and the nonlinear conditions on the finite end of the cylinder, the method of energy estimation is used to obtain the Phragmén-Lindelöf alternative results of the equations. In the case of decay, in order to make the results meaningful, the upper bound of total energy is established.

Key words: heat equation, Phragmén-Lindelö, f alternative, energy estimate, nonhomogeneous Neumann boundary condition

CLC Number: 

  • O175.29
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