This paper deals with the large-time behaviour of solutions to the fast diffusive Newtonian filtration equations coupled via the nonlinear boundary sources. A result of Fujita type is obtained by constructing various kinds of upper and lower solutions. In particular, it is shown that the critical global existence curve and the critical Fujita curve concide for the multi-dimensional system. This is quite different from the known results obtained in Wang, Zhou and Lou [‘Critical exponents for porous medium systems coupled via nonlinear boundary flux’, Nonlinear Anal.7(1) (2009), 2134–2140] for the corresponding one-dimensional problem.
