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

被引：5
作者：
Tunitsky, D. V. [1 ]
机构：
[1] Russian Acad Sci, VA Trapeznikov Inst Control Sci, Moscow, Russia
来源：
IZVESTIYA MATHEMATICS | 2023年 / 87卷 / 04期
基金：
俄罗斯基础研究基金会; 俄罗斯科学基金会;
关键词：
the Kolmogorov-Petrovskii-Piskunov-Fisher equation; second-order parabolic equation; semilinear equation on manifold; weak solution; stabilization;
D O I：
10.4213/im9354e
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：817 / 834
页数：18
相关论文
共 24 条
[11]  
Krein M.G., 1948, Usp. Mat. Nauk (N.S.), V3, P3
[12]  
Lieberman G. M., 1996, Second Order Parabolic Differential Equations
[13]  
Lions J. L., 1961, Die Grundlehren der mathematischen wissenschaften, V111
[14]  
NICOLAESCU L. I, 2021, Lectures on the Geometry of Manifolds
[15]  
Palais R. S., 1970, Ann. of Math. Stud., V57
[16]  
Perelman G., 2002, arXiv
[17]  
Perelman G, 2003, Arxiv, DOI [arXiv:math/0307245, DOI 10.48550/ARXIV.MATH/0307245]
[18]  
Perelman G, 2003, Arxiv, DOI arXiv:math/0303109
[19]  
Perthame B., 2015, Lecture Notes on Mathematical Modelling in the Life Sciences, pxii+199
[20]   MONOTONE METHODS IN NONLINEAR ELLIPTIC AND PARABOLIC BOUNDARY-VALUE PROBLEMS [J].
SATTINGER, DH .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1972, 21 (11) :979-+
123