本文研究高阶半线性抛物型方程组{ut+(-△)^m u=|v|^p,(t,x)∈R^1+×R^N,vt+(-△)^m v=|u|^q,(t,x)∈R^1+×R^N, u(0,x)=u0(x),v(0,x)=vo(x),z∈R^N,其中m,P,q〉1.利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度[0,T)给出估计.
This paper studies the higher-order semilinear parabolic system{ut+(-△)^m u=|v|^p,(t,x)∈R^1+×R^N,vt+(-△)^m v=|u|^q,(t,x)∈R^1+×R^N, u(0,x)=u0(x),v(0,x)=vo(x),z∈R^N,where m,p,q 〉 1, By virtue of the test function method, the authors first derive some integral inequalities, and then give the estimate of the life span [0, T) of blow-up solution.