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带时空积分源项的耦合抛物方程的爆破
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Abstract:
本文研究一个带时空积分源项的耦合抛物方程。通过线性变换，利用固定模问题的特征函数方法给出四个带系统解的特殊函数的导数之间的关系，并且构造合适辅助函数得到系统解发生爆破的充分条件；根据时空积分源项在时间初始时为零的特性构造出恰当的爆破的下解，给出系统解爆破的充分条件以及爆破时刻的上界；选取合适的整体存在的上解给出系统解整体存在的充分条件。
In this paper, a Coupled Parabolic Equation with time-space integral source term is studied. Through linear transformation, the relationship between the derivatives of four special functions with system solutions is given by using the characteristic function method of fixed mode problem, and the sufficient conditions for the blow-up of system solutions are obtained by constructing appropriate auxiliary functions; According to the characteristic that the source term of space-time integration is zero at the beginning of time, an appropriate blow-up lower solution is constructed, and the sufficient conditions for the blow-up of the system solution and the upper bound of the blow-up time are given; The sufficient conditions for the global existence of the solution of the system are given by selecting the appropriate upper solution of the global existence.
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