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

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

Abstract

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

CLC Number:

O175.26

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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