On absence of global solutions of quasilinear differential-convolutional inequalities

From a unique viewpoint, elliptic and parabolic second-order inequalities with quasilinear KPZ-type terms and nonlocal convolutional terms arising in the description of reaction–diffusion processes, neural networks, and nonlocal phase transitions are investigated. Sufficient conditions of the absence of their global solutions, i.e. necessary conditions of their global solvability, are found. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.