Absence of global solutions to systems of perturbed parabolic inequalities with Chipot-Weissler nonlinearity in the gradient term

For a wide class of systems of nonlinear parabolic inequalities with Chipot- Weissler nonlinearity in the gradient term which depend on two nonnegative parameters λ1 and λ2, we study the nonexistence of global solutions according to the "test function" method. We establish theorems that, when λ1 = λ2 = 0, include and, in some cases, improve, or, in part, yield the results obtained by Escobedo and Herrero; Escobedo and Levine; Galaktionov;Levine, Lieberman and Meier; Mitidieri and Pohozaev; Pohozaev and Tesei.