二元混合物中的热传导方程Phragmén-Lindelöf二择性

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

考虑定义在一个半无穷柱体上二元混合物中的热传导方程,其中柱体的母线平行于坐标轴。假设方程在柱体的侧面上满足非齐次Neumann边界条件,在柱体的有限端满足非线性条件,运用能量估计的方法,得到了方程的Phragmén-Lindelöf二择性结果。在衰减的情形下,为了使结果有意义,建立全能量的上界。

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.