局部非线性边界条件下热量方程解的空间渐近性

Spatial Asymptotic Behavior of Solutions of Heat Equationunder Locally Nonlinear Boundary Conditions

考虑非标准边界条件下热量方程在一个半无穷柱体上的渐近行为,其中解在侧面的局部区域满足齐次Neumann条件,在其他区域满足非齐次Neumann条件.用能量分析方法得到了该方程解的空间渐近定理,并把所得结果拓展到二元混合物中的热量方程上.

We considered the asymptotic behavior of the heat equation on a semi infinite cylinder under nonstandard boundary conditions,where the solution satisfied the homogeneous Neumann condition in the local region on the side and the non-homogeneous Neumann condition in the other regions.Using the energy analysis method,we obtained the spatial asymptotic theorem of the solution of the equation,and extended results to the heat equation in binary mixtures.