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.
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页码：2507 / 2513
页数：7
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