Secondary critical exponent and life span for a nonlocal parabolic p-Laplace equation

Abstract

This paper deals with positive solutions of the Cauchy problem for a parabolic p-Laplace equation with weighted nonlocal sourceswhere , , q, , , and . We classify global and non-global solutions of the Cauchy problem in the coexistence region by seeking a second critical exponent via the slow decay asymptotic behavior of an initial data at spatial infinity. Moreover, the large time behavior of global solution and the life span of non-global solution are derived.