一类非线性耦合抛物型方程组解的整体不存在性  

Nonexistence of Solutions for a Coupled Parabolic Systems with Source Terms

作　　者：裴金仙[1] PEI Jin-xian(Dept. of Mathematics, Business College of Shanxi University, Taiyuan 030031, China)

机构地区：[1]山西大学商务学院理学系,山西太原030031

出　　处：《中北大学学报（自然科学版）》2018年第3期255-259,共5页Journal of North University of China(Natural Science Edition)

摘　　要：研究了一类带有源项的非线性耦合抛物型方程组.该系统可以描述受到热源作用的热扩散系统或受到外部源项的反应扩散系统.由于源项的出现,使得系统不稳定,出现爆破现象.通过构造合适的泛函和合适的凸性不等式,证明了当初值和源项等满足一定的条件时,且源项的作用效果强于扩散项的作用效果时,系统的解将在有限时刻爆破,而且给出了爆破时刻上界的估计.A nonlinear coupled parabolic equations system with source terms was studied. This system can describe describe the processes of heat diffusion and combustion which was subjected to external force. The system will blow up since the source terms appear. It is proved that the solution of the cou- pled parabolic system is global nonexistence when the initial values and the nonlinear source terms satis- fy appropriate conditions by constructing suitable functional and suitable convex inequality. The estima- tion of the blow-up time is given.

关 键 词：耦合抛物型系统 源项 有限时刻爆破 爆破时刻估计 

分 类 号：O175[理学—数学]