This article is cited in 6 papers

On stabilization of solutions of second-order semilinear parabolic equations on closed manifolds

D. V. Tunitsky

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow

Abstract: The paper is concerned with problems of existence, uniqueness, and stabilization of weak solutions of one class of semilinear second-order parabolic differential equations on closed manifolds. These equations are inhomogeneous analogues of the Kolmogorov–Petrovskii–Piskunov–Fisher equation, and have significant applied and mathematical value.

Keywords: the Kolmogorov–Petrovskii–Piskunov–Fisher equation, second-order parabolic equation, semilinear equation on manifold, weak solution, stabilization.

UDC: 517.956.4+517.956.8+517.955

MSC: Primary 35L70; Secondary 35L60, 58A17

Received: 11.06.2022

DOI: 10.4213/im9354

 English version: Izvestiya: Mathematics, 2023, 87:4, 817–834

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