Fujita Type Results for a Parabolic Inequality With a Nonlinear Convolution Term on the Heisenberg Group

The purpose of this paper is to investigate the nonexistence of global weak solutions to a class of degenerate inequalities posed on the Heisenberg group. Specifically, we consider an evolution inequality involving the Heisenberg Laplacian with a nonlocal in space nonlinearity where the initial data belongs to the local Lebesgue space. Our approach is based on the nonlinear capacity method, which allows us to establish nonexistence results under certain conditions on the parameters involved.