一类交叉耦合抛物方程组解的整体存在及爆破

doi:10.3969/j.issn.1000-1565.2017.04.002一类交叉耦合抛物方程组解的整体存在及爆破

河北大学学报(自然科学版) ›› 2017, Vol. 37 ›› Issue (4): 343-348.DOI: 10.3969/j.issn.1000-1565.2017.04.002一类交叉耦合抛物方程组解的整体存在及爆破

一类交叉耦合抛物方程组解的整体存在及爆破

薛应珍

收稿日期:2017-02-21 出版日期:2017-07-25 发布日期:2017-07-25
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理论及应用的研究. E-mail:xueyingzhen@126.com
基金资助:
陕西省自然科学基础研究计划项目(2016JM1036);陕西省教育科学十三五规划课题(SGH16H292)

Global existence and blow up problem for a parabolic equations cross coupled terms

XUE Yingzhen

College of Business, Xi'an International University, Xi'an 710077, China

Received:2017-02-21 Online:2017-07-25 Published:2017-07-25

摘要/Abstract

摘要： 为了更好描述3种混合物质燃烧的热传导过程,或者化学反应中3种反应物的反应情况,研究了一类具有3个变量交叉耦合且带有非局部源及非局部边界流抛物型方程组解的整体存在及有限时刻爆破问题,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局部源和指数函数非局部源交叉耦合的退化抛物型方程组解的整体存在及解在有限时刻爆破的充分条件,为热传导和化学反应问题提供更好的理论支持.

关键词: 交叉抛物型方程组, 比较原理, 整体存在, 爆破

Abstract: In order to better describe the heat transfer process of three kinds of mixed substances, or the reaction of the reactants in the three chemical reactions,a class of three variable cross coupling with non parabolic equations of the whole existence of local source and non local boundary flow and the finite time blow up problem with breaking method for the solution of the first commonly used feature value structure are studied, and the structure of the equations of the upper and lower solutions by using the method of ordinary differential equation reference, comparison theorem, the proof obtained by local source power function and exponential function of parabolic equations and the sufficient conditions for global existence of solutions blow up in finite time degradation of non local sources of cross coupling, provide better support for the theory of heat transfer and chemical reaction problem.

Key words: parabolic equations cross coupled terms, the comparison principle, global solution, blow up

中图分类号:

O175.26

薛应珍. 一类交叉耦合抛物方程组解的整体存在及爆破[J]. 河北大学学报(自然科学版), 2017, 37(4): 343-348.

XUE Yingzhen. Global existence and blow up problem for a parabolic equations cross coupled terms[J]. Journal of Hebei University (Natural Science Edition), 2017, 37(4): 343-348.

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一类交叉耦合抛物方程组解的整体存在及爆破

Global existence and blow up problem for a parabolic equations cross coupled terms

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