一类交叉耦合抛物型方程组解的渐近性态

Asymptotic behavior for cross coupled parabolic equations

为了更好地描述3种混合物质燃烧的热传导过程,即3种化学反应中反应物的反应情况,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和有限时刻爆破问题,打破常用的第一特征值的构造上下解的方法,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了理论支持。

In order to better describe the heat transfer process of three kinds of mixed substances,namely 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.The structure of the equations of the upper and lower solutions by using the method of ordinary differential equation reference is broken,with comparison theorem,the proof shows that obtained by local source power function and exponential function of parabolic equations is broken,with the sufficient conditions for global existence of clegerate purubolic equations solutions cross coupled by local source power function and non local sources exponential function are proved,as soon as the solution of blowing up in finite time degradation of non local sources of cross coupling,providing better support for the theory of heat transfer and chemical reaction problem.