UNIQUENESS OF NONZERO POSITIVE SOLUTIONS OF LAPLACIAN ELLIPTIC EQUATIONS ARISING IN COMBUSTION THEORY
UNIQUENESS OF NONZERO POSITIVE SOLUTIONS OF LAPLACIAN ELLIPTIC EQUATIONS ARISING IN COMBUSTION THEORY
复制标题
燃烧理论中拉普拉斯椭圆方程非零正解的唯一性
DOI：
10.3934/dcdsb.2016.21.849
复制
发表时间：
2016-05-01
影响因子：
1.2
通讯作者：
Lin, Wei
中科院分区：
文献类型：
--
作者：
Lan, Kunquan;Lin, Wei
燃烧理论中出现的拉普拉斯椭圆方程非零正解的唯一性在燃烧理论中引起了极大的兴趣，因为它可以应用于确定灭绝现象发生的位置。只要反应速率的阶数在 (-无穷大, 1] 内，我们就研究唯一性。以前的唯一性结果处理阶数属于 [0, 1) 的情况。当阶数为负或1时，具有物理意义，双分子反应速率对应阶数1，但关于唯一性的研究很少。当阶数为负或 1 时，我们关于唯一性的结果是全新的，并且当阶数属于 (0, 1) 时，我们还改进了一些已知的结果。我们的结果提供了弗兰克-卡梅涅茨基参数的精确区间，在该区间内绝灭现象永远不会发生。我们方法的新颖之处在于，结合并利用拉普拉斯椭圆不等式和方程的结果，得出关于一般拉普拉斯椭圆方程非零正解的唯一性的新结果。
Uniqueness of nonzero positive solutions of a Laplacian elliptic equation arising in combustion theory is of great interest in combustion theory since it can be applied to determine where the extinction phenomenon occurs. We study the uniqueness whenever the orders of the reaction rates are in (-infinity, 1]. Previous results on uniqueness treated the case when the orders belong to [0, 1). When the orders are negative or 1, it is physically meaningful and the bimolecular reaction rate corresponds to the order 1, but there is little study on uniqueness. Our results on the uniqueness are completely new when the orders are negative or 1, and also improve some known results when the orders belong to (0, 1). Our results provide exact intervals of the Frank-Kamenetskii parameters on which the extinction phenomenon never occurs. The novelty of our methodology is to combine and utilize the results from Laplacian elliptic inequalities and equations to derive new results on uniqueness of nonzero positive solutions for general Laplacian elliptic equations.