EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

数学物理学报(英文版) ›› 2000, Vol. 20 ›› Issue (4): 451-460.

EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

戴正德, 蒋慕容

Department of Mathematics, Yunnan University, Kunming 650091, China

收稿日期:1998-08-25 出版日期:2000-06-15 发布日期:2000-06-15
基金资助:
Project supported by the National Natural Science Foundation of China
(No:19861004)

EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

DAI Zheng-De, JIANG Mu-Rong

Department of Mathematics, Yunnan University, Kunming 650091, China

Received:1998-08-25 Online:2000-06-15 Published:2000-06-15
Supported by:
Project supported by the National Natural Science Foundation of China
(No:19861004)

摘要/Abstract

摘要：

The equation of pattern formation induced by buoyancy or by surface-tension
gradient in finite systems confined between horizontal poor heat conductors is introduced
by Knobloch[1990]
@u
@t
= u − μ∇2u − ∇4u + K∇ · (|∇u|2∇u + ∇2u∇u −
u∇u + ∇|∇u|2)
where u is the planform function, μ is the scaled Rayleigh number, K = 1 and represents
the effects of a heat transfer finite Biot number. The cofficients , and
do not vanish
when the boundary conditions at top and bottom are not identical ( 6= 0, 6= 0) or non-
Boussinesq effects are taken into account (
6= 0). In this paper, the Knobloch equation
with > 0 is considered, the global existence in L2-space and the finite existence time of
solution in V 2-space have been obtained respectively.

关键词: Knobloch equation, initial-boundary value problem, blow-up, global exis-
tence

Abstract:

Key words: Knobloch equation, initial-boundary value problem, blow-up, global exis-
tence

中图分类号:

戴正德, 蒋慕容. EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM[J]. 数学物理学报(英文版), 2000, 20(4): 451-460.

DAI Zheng-De, JIANG Mu-Rong. EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM[J]. Acta mathematica scientia,Series B, 2000, 20(4): 451-460.

参考文献

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EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

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