School of Mathematical Science;
Dalian University of Technology;
Liaoning 116024;
P. R. China;
Geomathematics Key Laboratory of Sichuan Province;
Chengdu University of Technology;
Sichuan 610059;
P. R. China;
quasilinear parabolic system; nonlocal boundary conditions; critical exponent; blow-up rate; weight functions.;