伪抛物方程组解的全局存在
Global existence of solution to pseudo-parabolic system

研究如下非线性伪抛物方程组柯西问题解的全局存在性，ut－Δut=Δu+uαvp，vt－Δvt=Δv+uqvβ，这里p，q≥0，α，β≥0. 首先应用压缩映射原理得到解的局部存在性，之后运用上下解方法研究α，β≤1，pq≤（1－α）（1－β）时解的全局存在性.
This paper deals with the Cauchy problem to nonlinear pseudo-parabolic system ut－Δut=Δu+uαvp，vt－Δvt=Δv+uqvβ where，q≥0，α，β≥0. we first applied contraction mapping to obtain that local solutions are existence. And then we investigate that the solutions are global while α，β≤1and pq≤（1－α）（1－β） by use upper and lower solutions method