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

[1] ON THE SET OF SOLUTIONS TO A SEMI-LINEAR PARABOLIC EQUATION
LASRY, JM
TROIANIELLO, GM
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1982, 7 (09) : 1001 - 1021
[2] NUMERICAL SOLUTIONS FOR SINGULARLY PERTURBED SEMI-LINEAR PARABOLIC EQUATION
吴启光
李继春
Applied Mathematics and Mechanics(English Edition), 1993, (09) : 793 - 801
[3] Optimal lower bound of the grow-up rate for a supercritical parabolic equation
Fila, Marek
King, John R.
Winkler, Michael
Yanagida, Eiji
JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 228 (01) : 339 - 356
[4] Grow-up rate of solutions for the heat equation with a sublinear source
Wang, Liangwei
Yin, Jingxue
BOUNDARY VALUE PROBLEMS, 2012,
[5] Grow-up rate of solutions for a supercritical semilinear diffusion equation
Fila, M
Winkler, M
Yanagida, E
JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 205 (02) : 365 - 389
[6] Grow-up rate of solutions for the heat equation with a sublinear source
Liangwei Wang
Jingxue Yin
Boundary Value Problems, 2012
[7] STABILITY OF STATIONARY SOLUTIONS OF A SEMI-LINEAR PARABOLIC PARTIAL-DIFFERENTIAL EQUATION
MAGINU, K
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1978, 63 (01) : 224 - 243
[8] Blow-up or Grow-up for the threshold solutions to the nonlinear Schrodinger equation
Gustafson, Stephen
Inui, Takahisa
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2023, 20 (03) : 213 - 225
[9] Grow-up on the boundary for a semilinear parabolic problem
Fila, M
Velázquez, JJL
Winkler, M
Nonlinear Elliptic and Parabolic Problems: A SPECIAL TRIBUTE TO THE WORK OF HERBERT AMANN, MICHEL CHIPOT AND JOACHIM ESCHER, 2005, 64 : 137 - 150
[10] The asymptotic behavior of the solutions of semi-linear parabolic equation in semi-infinite cylindrical domain
Filimonova, I.V.
Doklady Akademii Nauk, 2005, 400 (02) : 166 - 168

← 1 2 3 4 5 →