Abstract:

The authors investigated the global existence and blowup properties of nonnegative solutions for a class of nonlocal parabolic systems
with nonlocal boundary conditions. With the help of  the super and subsolution methods, the critical exponent of system was gained. And it’s proved that if p=(p₁+q₁)…(p_k+q_k)-1,p≤0 and 0≤∫_Ωψ_i(x,y)dy<1, every nonnegative solution is global, whereas if p>0, then the solution blows\|up in finite time if the initial data is sufficiently large. Moveover, the exact rate of the blow\|up is obtained. The results show that the size of initial values and exponents play an important role in the properties of the solutions.

Key words: parabolic system, global existence, blowup; , blowup rate