Cauchy problem for a non-Newtonian filtration equation with slowly decaying volumetric moisture content

This article is concerned with the qualitative properties for the Cauchy problem of a non-Newtonian filtration equation with a reaction source term and volumetric moisture content. On the basis of the slowly decaying behavior of volumetric moisture content, we establish new critical exponents that depend on the ratio of coefficients and exponent of volumetric moisture content. Meantime, under appropriate conditions, we show that the solution globally exists for small enough initial data and blows up in finite time for large enough or any nontrivial initial datum.