一类多孔介质抛物型方程组解的渐近性态

doi:10.3969/j.issn.1000-1565.2019.05.001

河北大学学报(自然科学版) ›› 2019, Vol. 39 ›› Issue (5): 449-454.DOI: 10.3969/j.issn.1000-1565.2019.05.001

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一类多孔介质抛物型方程组解的渐近性态

薛应珍¹,冯贺平²

收稿日期:2019-02-15 出版日期:2019-09-25 发布日期:2019-09-25
作者简介:薛应珍(1980—),男,甘肃庆阳人,西安外事学院副教授,主要从事偏微分方程研究. E-mail:xueyingzhen@126.com
基金资助:
陕西省自然科学基础研究计划项目(2019JM-534);陕西省社科界重大理论与现实问题研究项目(2019C135);陕西省教育科学“十三五”规划课题(SGH18H544);陕西省高等教育学会课题(XGH17208)

Asymptotic properties for a porous media parabolic equations

XUE Yingzhen¹,FENG Heping²

1.School of Business, Xian International University, Xian 710077, China; 2.Intelligent Engineering Department, Hebei Software Institute, Baoding 071000, China

Received:2019-02-15 Online:2019-09-25 Published:2019-09-25

摘要/Abstract

摘要： 为了描述物理学中多孔介质力学、流体力学、气体流量等问题3种介质的反应扩散问题,研究了一类具有3个变量耦合且同时具有加权非局部边界和非线性内部源的多孔介质抛物型方程组解的渐近性态,打破常用的第一特征值等构造上下解的方法,而采用常微分方程方法构造了该方程组的上、下解,引用比较定理,证明得到了由幂函数和指数函数完全耦合的一类抛物型方程组解的存在及爆破问题,在推广了已有的结果的基础上,为多孔介质及流体力学等问题提供理论支持.

关键词: 多孔介质抛物方程组, 比较原理, 整体存在, 爆破

Abstract: In order to describe the reaction diffusion problems of three media in physics, such as mechanics of porous media, fluid mechanics, gas flow and so on, the asymptotic behavior of a class of parabolic equations of porous media,with 3 variables coupled with a weighted nonlocal boundary and a nonlinear internal source is studied.The upper and lower solutions of the first eigenvalue are broken, and the upper and lower solutions of the equations are constructed by using the ordinary differential equation method, and the comparison theorem is quoted. It is proved that the whole existence of the solution of the parabolic equations of porous media with the power function and the exponential function fully coupled and the sufficient conditions for the solution in the finite time blasting are obtained.On the basis of the existing results, provide more theoretical support for porous media and fluid mechanics are achieved.

Key words: porous media parabolic equations, the comparison principle, global solution, blow up

中图分类号:

O175.29

薛应珍,冯贺平. 一类多孔介质抛物型方程组解的渐近性态[J]. 河北大学学报(自然科学版), 2019, 39(5): 449-454.

XUE Yingzhen,FENG Heping. Asymptotic properties for a porous media parabolic equations[J]. Journal of Hebei University (Natural Science Edition), 2019, 39(5): 449-454.

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一类多孔介质抛物型方程组解的渐近性态

Asymptotic properties for a porous media parabolic equations

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