具有非线性边界条件的瞬态热传导方程的二择一结果

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1248-1258.

具有非线性边界条件的瞬态热传导方程的二择一结果

李远飞*(),李志青()

^{广东财经大学华商学院应用数学系广州 511300}

收稿日期:2019-08-27 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 李远飞 E-mail:liqfd@163.com;1032170427@qq.com
作者简介:李志青, E-mail:1032170427@qq.com
基金资助:
广东省普通高校重点项目（自然科学）(2019KZDXM042);广东省自然科学基金(2017A030313037)

Phragmén-Lindelöf Type Results for Transient Heat Conduction Equation with Nonlinear Boundary Conditions

Yuanfei Li*(),Zhiqing Li()

^{Department of Applied Mathematics, Huashang College, Guangdong University of Finance Economics, Guangzhou 511300}

Received:2019-08-27 Online:2020-10-26 Published:2020-11-04
Contact: Yuanfei Li E-mail:liqfd@163.com;1032170427@qq.com
Supported by:
the Key Projects of Universities in Guangdong Province (Nature Science)(2019KZDXM042);the Guangdong Natural Science Foundation(2017A030313037)

摘要/Abstract

摘要：

考虑了定义在三维半无限柱体上的瞬态热传导方程，其中在柱体的有限端和侧面施加了非线性条件.通过对边界条件做出一定约束之后，建立了关于"能量表达式"的一个偏微分不等式，并由此不等式得到了热传导方程的二择一结果.在衰减的情况下，证明了"全能量"可以由已知数据项控制.

关键词: 热传导方程, 空间衰减性, 二择一, 能量估计

Abstract:

The transient heat conduction equation defined in a three-dimensional semi-infinite cylinder is Considered, in which the nonlinear conditions are imposed on the finite end and the lateral surface of the cylinder. A partial differential inequality for the "energy expression" is established after some constraints are imposed on the boundary conditions, and Phragmén-Lindelöf type results of the heat conduction equation is obtained from the inequality. In the case of decay, it is proved that "total energy" can be controlled by known data.

Key words: Heat conduction equation, Spatial decay estimates, Phragmén-Lindelöf, Energy estimates

中图分类号:

O175.29

李远飞,李志青. 具有非线性边界条件的瞬态热传导方程的二择一结果[J]. 数学物理学报, 2020, 40(5): 1248-1258.

Yuanfei Li,Zhiqing Li. Phragmén-Lindelöf Type Results for Transient Heat Conduction Equation with Nonlinear Boundary Conditions[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1248-1258.

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