Global existence and nonexistence for an inhomogeneous quasilinear convection‐diffusion equation

Abstract This paper deals with the qualitative properties of solutions to the Cauchy problem for a quasilinear convection–diffusion equation with volumetric moisture content, which involves the cases of critical and fast decaying volumetric moisture content. Based on the method of directly constructing Barenblatt‐type super‐ and sub‐solutions, we establish the new criteria of global existence and nonexistence and provide the properties of expansion and shrinking of the support of the weak solution.