On absence of global solutions of quasilinear differential-convolutional inequalities. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Muravnik, A. B.
• Is Part Of: Complex variables and elliptic equations. Volume 65:Issue 6(2020)
• Page Start: 977
• Page End: 985
• Publication Date: 2020-06-02
• Subjects: V. Volpert; Quasilinear inequalities -- convolutional terms -- nonlocal terms -- global solutions -- nonexistence; 34K38 -- 35A01; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2019.1639049
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: 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.