Nonclassical stationary and nonstationary problems with weight Neumann conditions for singular equations with KPZ-nonlinearities

From a unique viewpoint, singular elliptic and parabolic second-order inequalities with quasilinear KPZ-type terms are investigated in cylindrical domains. The weight Neumann condition is set on the lateral area of the cylinder; no condition is set on the base of the cylinder (regardless the type of the equation). Results of two kinds are established: the existence of a limit of each solution (if it exists) along the axis of the cylinder and sufficient conditions of a blow-up (including instant or complete one). © 2020 Informa UK Limited, trading as Taylor & Francis Group.