VERY SLOW GROW-UP OF SOLUTIONS OF A SEMI-LINEAR PARABOLIC EQUATION

被引：2

作者：

Fila, Marek ^{[1
]}

King, John R. ^{[2
]}

Winkler, Michael ^{[3
]}

Yanagida, Eiji ^{[4
]}

机构：

[1] Comenius Univ, Dept Appl Math & Stat, Bratislava 84248, Slovakia

[2] Univ Nottingham, Div Theoret Mech, Nottingham NG7 2RD, England

[3] Univ Duisburg Essen, Fachbereich Math, D-45117 Essen, Germany

[4] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2011年 / 54卷

关键词：

grow-up; semi-linear parabolic equation; comparison principle; HEAT-EQUATION; SUPERCRITICAL NONLINEARITY; CONVERGENCE; ZERO;

D O I：

10.1017/S0013091509001497

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider large-time behaviour of global solutions of the Cauchy problem for a parabolic equation with a supercritical nonlinearity. It is known that the solution is global and unbounded if the initial value is bounded by a singular steady state and decays slowly. In this paper we show that the grow-up of solutions can be arbitrarily slow if the initial value is chosen appropriately.

引用

页码：381 / 400

页数：20

共 50 条

[41] Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold
Gu, Qingsong
Sun, Yuhua
Xiao, Jie
Xu, Fanheng
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (05)
[42] PULLBACK ATTRACTORS FOR A NON-AUTONOMOUS SEMI-LINEAR DEGENERATE PARABOLIC EQUATION
Cung The Anh
Tang Quoc Bao
GLASGOW MATHEMATICAL JOURNAL, 2010, 52 : 537 - 554
[43] Painleve analysis for a semi-linear parabolic equation arising in smectic liquid crystals
Stewart, IW
IMA JOURNAL OF APPLIED MATHEMATICS, 1998, 61 (01) : 47 - 60
[44] Bounded Solutions of Semi-Linear Parabolic Differential Equations with Unbounded Delay Terms
Ashyralyev, Allaberen
Mu'azu, Sa'adu Bello
MATHEMATICS, 2023, 11 (16)
[45] A PROBABILISTIC TREATMENT OF SEMI-LINEAR PARABOLIC EQUATIONS
SIRAO, T
PROCEEDINGS OF THE JAPAN ACADEMY, 1966, 42 (08): : 885 - &
[46] Composition Method for Semi-linear Parabolic Systems
Bondarenko V.
Markevych I.
International Journal of Applied and Computational Mathematics, 2024, 10 (2)
[47] Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions
R. Ferreira
A. de Pablo
Revista Matemática Complutense, 2018, 31 : 805 - 832
[48] Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions
Ferreira, R.
de Pablo, A.
REVISTA MATEMATICA COMPLUTENSE, 2018, 31 (03): : 805 - 832
[49] A CLASSIFICATION OF SOLUTIONS OF A FOURTH ORDER SEMI-LINEAR ELLIPTIC EQUATION IN Rn
Chammakhi, Ridha
Harrabi, Abdellaziz
Selmi, Abdelbaki
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2017, 30 (7-8) : 569 - 586
[50] Regional stabilization of semi-linear parabolic systems
El Harraki, I.
El Alami, A.
Boutoulout, A.
Serhani, M.
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2017, 34 (03) : 961 - 971

← 1 2 3 4 5 →