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

Author

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  • Andrey B. Muravnik

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

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.

Suggested Citation

  • Andrey B. Muravnik, 2023. "Qualitative Properties of Solutions of Equations and Inequalities with KPZ-Type Nonlinearities," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:990-:d:1069252
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    Cited by:

    1. Andrey B. Muravnik, 2023. "Keller–Osserman Phenomena for Kardar–Parisi–Zhang-Type Inequalities," Mathematics, MDPI, vol. 11(17), pages 1-7, September.
    2. Sergei Sitnik, 2023. "Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”," Mathematics, MDPI, vol. 11(15), pages 1-7, August.

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