| 一类多方渗流方程正解的存在性和爆破性 |
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| 引用本文： | 李建军,唐依纳.一类多方渗流方程正解的存在性和爆破性[J].应用数学和力学,2021,42(9):924-931. |
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| 作者姓名： | 李建军 唐依纳 |
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| 作者单位： | 辽宁工程技术大学 理学院， 辽宁 阜新 123000 |
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| 摘 要： | 该文研究了一类具有非局部Neumann边界条件和非线性吸收项的多方渗流方程解的全局存在性和爆破情况.首先针对所研究方程定义了其上下解，并建立和证明了比较原理；然后通过构造函数以及利用微分不等式、特征值特征函数、常微分方程的解和椭圆第二边值的解等方法对方程进行了研究，得到了对于不同取值范围的参数、权函数和初始值时，方程非负解的全局存在性和在有限时间内爆破的充分条件.
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| 关 键 词： | Neumann边界条件 多方渗流方程 全局存在性 爆破 |
| 收稿时间： | 2021-01-21 |
Existence and Blowup of Positive Solutions to a Class of Multilateral Flow Equations |
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| Affiliation: | Existence and Blowup of Positive Solutions to a Class of Multilateral Flow Equations |
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| Abstract: | The global existence and blowup of the solutions to a class of multilateral filtration equations with non-local Neumann boundary conditions and nonlinear absorption terms were studied. First, the super- and sub-solutions were defined for the studied equations and the comparison principle was established. Then, the equation was investigated with constructed functions, differential inequalities, eigenfunctions, ordinary differential equation and elliptic second boundary value solutions. The global existence of non-negative solutions to the equations and the conditions for blowup in a finite time for the parameters, weight functions and initial values in different value ranges were obtained. |
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