The asymptotic properties of solutions to a multi-dimensional Newtonian filtration equations

AbstractThis paper deals with the exterior problem of the multidimensional Newtonian filtration equations coupled via nonlinear boundary flux. The asymptotic properties of solutions including the critical global existence curve and the critical Fujita curve are determined. In particular, an interesting phenomenon is shown, there exists a threshold value for the spacial dimension such that the critical global existence curve and the critical Fujita curve are the same when the spacial dimension , while these two critical curves are entirely different when .