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In these years, semilinear reaction-diffusion systems of the Fujita typeut=Δu+vm(A)vt Δ v + un, (x,t) ∈Ω× (0,T),as well as the related elliptic systemswith the region Ω Rn RN, m ,n ＞ 1 were studied by a number of authors, The problems concerning (A)