ASYMPTOTIC AND QUENCHING BEHAVIORS OF SEMILINEAR PARABOLIC SYSTEMS WITH SINGULAR NONLINEARITIES

被引：2

作者：

Wang, Qi ^{[1
]}

Zhang, Yanyan ^{[2
]}

机构：

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[2] East China Normal Univ, Sch Math Sci, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2022年 / 21卷 / 03期

关键词：

semilinear parabolic system; singular nonlinearity; global existence; quenching; convergence rate; EQUATIONS;

D O I：

10.3934/cpaa.2021199

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a family of parabolic systems with singu-lar nonlinearities. We study the classification of global existence and quenching of solutions according to parameters and initial data. Furthermore, the rate of the convergence of the global solutions to the minimal steady state is given. Due to the lack of variational characterization of the first eigenvalue to the lin-earized elliptic problem associated with our parabolic system, some new ideas and techniques are introduced.

引用

页码：797 / 816

页数：20

共 50 条

[21] QUENCHING BEHAVIOR OF SEMILINEAR HEAT EQUATIONS WITH SINGULAR BOUNDARY CONDITIONS
Selcuk, Burhan
Ozalp, Nuri
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[22] Exponential stabilization of semilinear parabolic systems
El Harraki, Imad
Lamrani, Ilyasse
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2023, 360 (11): : 7294 - 7324
[23] Convergence rate to singular steady states in a semilinear parabolic equation
Hoshino, Masaki
Yanagida, Eiji
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 131 : 98 - 111
[24] Simultaneous and non-simultaneous quenching for a coupled semilinear parabolic system in a n-dimensional ball with singular localized sources
Chan, W. Y.
AIMS MATHEMATICS, 2021, 6 (07): : 7704 - 7718
[25] Critical singular exponent and asymptotic estimates in the parabolic equations
Liu, Bingchen
Li, Fengjie
APPLIED MATHEMATICS LETTERS, 2017, 65 : 63 - 69
[26] BACKWARD SDEs AND SOBOLEV SOLUTIONS FOR SEMILINEAR PARABOLIC PDEs WITH SINGULAR COEFFICIENTS
Zhang, Tusheng
Ran, Qikang
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2011, 14 (03) : 517 - 536
[27] On regularity and asymptotic stability for semilinear nonlocal pseudo-parabolic equations
Quyet, Dao Trong
Thanh, Dang Thi Phuong
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2024, 43 (1-2): : 67 - 88
[28] Asymptotic self-similar behavior of solutions for a semilinear parabolic system
Snoussi, S
Tayachi, S
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2001, 3 (03) : 363 - 392
[29] Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs
Zhu, Liping
Zhou, Yaxin
Huang, Lin
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2024, 37 (01): : 104 - 120
[30] The quenching behavior of a nonlinear parabolic equation with a singular boundary condition
Ozalp, Nuri
Selcuk, Burhan
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2015, 44 (03): : 615 - 621

← 1 2 3 4 5 →