Critical exponents for a non‐Newtonian polytropic filtration equation with weighted nonlocal inner sources

Abstract

This article considers the Cauchy problem for a non‐Newtonian polytropic filtration equation with weighted nonlocal inner sources where N ≥ 1, , 0<m ≤ 1, q>1, r ≥ 1, , and r+s>1. We first obtain a new critical Fujita exponent by virtue of the auxiliary function method and the forward self‐similar solution and then determine the second critical exponent to classify global and nonglobal solutions of the problem in the coexistence region via the decay rates of an initial data at spatial infinity. Moreover, the large time behavior of global solution and the life span of nonglobal solution are derived.