Qualitative Properties of Solutions of Equations and Inequalities with KPZ-Type Nonlinearities

Andrey B. Muravnik ()
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Andrey B. Muravnik: Nikol’skii Mathematical Institute, Peoples Friendship University of Russia, Miklukho–Maklaya ul. 6, Moscow 117198, Russia

Mathematics, 2023, vol. 11, issue 4, 1-16

Abstract: For quasilinear partial differential and integrodifferential equations and inequalities containing nonlinearities of the Kardar—Parisi—Zhang type, various (old and recent) results on qualitative properties of solutions (such as the stabilization of solutions, blow-up phenomena, long-time decay of solutions, and others) are presented. Descriptive examples demonstrating the Bitsadze approach (the technique of monotone maps) applied in this research area are provided.

Keywords: quasilinear equations and inequalities; KPZ-nonlinearities; qualitative properties of solutions; methods of monotonous maps; blow-up; stabilization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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