Abstract: The purpose of this paper is to study the existence and nonexistence of global solutions to the degenerate evolution inequalities with singular potential correlated to the generalized BaouendiGrushin operator. The obtained results extend and improve upon those in the literature. To prove the existence results, we used the method of supersolution and the modified Bessel function. The nonexistence results are established by means of the test function method.

Key words: generalized BaouendiGrushin vector fields, degenerate evolution inequality, potential