Global well-posedness, asymptotic behavior and blow-up of solutions for a class of degenerate parabolic equations

被引：4

作者：

Liu, Yang ^{[1
]}

Yu, Tao ^{[2
]}

Li, Wenke ^{[3
]}

机构：

[1] Northwest Minzu Univ, Coll Math & Comp Sci, Lanzhou 730124, Peoples R China

[2] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China

[3] Harbin Engn Univ, Coll Power & Energy Engn, Harbin 150001, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 196卷

关键词：

Degenerate parabolic equations; Global well-posedness; Asymptotic behavior; Blow-up; A family of potential wells; NEUMANN PROBLEMS; INDEFINITE; NONEXISTENCE; INSTABILITY;

D O I：

10.1016/j.na.2020.111759

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The initial-boundary value problem for a class of degenerate parabolic equations is studied. Some new results on global existence of solutions are established by introducing a family of potential wells. In addition, asymptotic behavior and finite time blow-up of solutions are obtained in the case of subcritical initial energy and critical initial energy, respectively. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：14

共 50 条

[21] Local well-posedness and blow-up criteria of solutions for a rod equation
Zhou, Y
MATHEMATISCHE NACHRICHTEN, 2005, 278 (14) : 1726 - 1739
[22] LOCAL WELL-POSEDNESS AND BLOW-UP OF SOLUTIONS FOR WAVE EQUATIONS ON SHALLOW WATER WITH PERIODIC DEPTH
Fan, Lili
Gao, Hongjun
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[23] Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations
Jeong, Eunji
Kim, Junha
Lee, Jihoon
ADVANCES IN MATHEMATICAL PHYSICS, 2018, 2018
[24] Behavior of blow-up solutions for quasilinear parabolic equations
Yevgenieva Y.A.
Journal of Mathematical Sciences, 2020, 249 (5) : 804 - 816
[25] On some global well-posedness and asymptotic results for quasilinear parabolic equations
McLeod, Kevin
Milani, Albert
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 1996, 3 (01): : 79 - 114
[26] Blow-up results of the positive solution for a class of degenerate parabolic equations
Dong, Chenyu
Ding, Juntang
OPEN MATHEMATICS, 2021, 19 (01): : 773 - 781
[27] Boundary blow-up solutions to a class of degenerate elliptic equations
Lee, Jihoon
ANALYSIS AND MATHEMATICAL PHYSICS, 2019, 9 (03) : 1347 - 1361
[28] Boundary blow-up solutions to a class of degenerate elliptic equations
Jihoon Lee
Analysis and Mathematical Physics, 2019, 9 : 1347 - 1361
[29] Blow-up solutions of degenerate parabolic problems
Sawangtong, P.
Jumpen, W.
WSEAS Transactions on Mathematics, 2010, 9 (09) : 723 - 733
[30] Semidiscretization in space of nonlinear degenerate parabolic equations with blow-up of the solutions
Ishiwata, T
Tsutsumi, M
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2000, 18 (06) : 571 - 586

← 1 2 3 4 5 →