BLOW-UP PHENOMENA FOR A CLASS OF FOURTH-ORDER PARABOLIC PROBLEMS

被引：23

作者：

Philippin, G. A. ^{[1
]}

机构：

[1] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V OA6, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 143卷 / 06期

关键词：

Fourth-order parabolic problems; Blow-up; Sobolev type inequality; EQUATIONS; NONEXISTENCE; INSTABILITY; THEOREMS;

D O I：

10.1090/S0002-9939-2015-12446-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with some qualitative properties of solutions to a class of semilinear fourth-order parabolic problems. It is shown that under certain conditions on the data, u(x, t) cannot exist for all time and an upper bound for t(star) is derived where (0, t(star)) is the interval of existence of u(x, t). Moreover we construct (under certain conditions on the data) a lower bound for t(star) when blow-up occurs. This last result is based on some Sobolev type inequality established at the end of the paper.

引用

页码：2507 / 2513

页数：7

共 50 条

[1] Blow-up phenomena for a class of fourth order parabolic equation
Shao, Xiangkun
Tang, Guo-ji
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 505 (01)
[2] Blow-Up Phenomena for a Fourth-Order Parabolic Equation with a General Nonlinearity
Han, Yuzhu
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2021, 27 (02) : 261 - 270
[3] Blow-Up Phenomena for a Fourth-Order Parabolic Equation with a General Nonlinearity
Yuzhu Han
Journal of Dynamical and Control Systems, 2021, 27 : 261 - 270
[4] Blow-up phenomena for a class of fourth-order nonlinear wave equations with a viscous damping term
Khelghati, Ali
Baghaei, Khadijeh
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (02) : 490 - 494
[5] On the blow-up of solutions for some fourth order parabolic equations
Cheng, Ting
Zheng, Gao-Feng
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (11) : 2500 - 2511
[6] BLOW-UP PHENOMENA FOR THE SIXTH-ORDER BOUSSINESQ EQUATION WITH FOURTH-ORDER DISPERSION TERM AND NONLINEAR SOURCE
Liu, Jinxing
Wang, Xiongrui
Zhou, Jun
Zhang, Huan
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2021, 14 (12): : 4321 - 4335
[7] Sufficient Conditions and Bounds Estimate of Blow-Up Time for a Fourth Order Parabolic Equation
Zhao, Lijing
Li, Fushan
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2022, 21 (03)
[8] On the blow-up of solutions to a fourth-order pseudoparabolic equation
Polat, Mustafa
TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (03) : 946 - 952
[9] Blow-up phenomena for some nonlinear parabolic problems
Payne, L. E.
Philippin, G. A.
Schaefer, P. W.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (10) : 3495 - 3502
[10] Blow-up, non-extinction and exponential growth of solutions to a fourth-order parabolic equation
Baghaei, Khadijeh
COMPTES RENDUS MECANIQUE, 2022, 350 (01): : 47 - 56

← 1 2 3 4 5 →