On the blow-up behavior of a nonlinear parabolic equation with periodic boundary conditions

被引：2

作者：

Cortissoz, Jean C. ^{[1
,2
]}

机构：

[1] Univ Los Andes, Dept Matemat, Bogota, Colombia

[2] Inst Colombiano Ciencias, Rincon Del Mar, Sucre, Colombia

来源：

ARCHIV DER MATHEMATIK | 2011年 / 97卷 / 01期

关键词：

Nonlinear parabolic equations; Periodic boundary conditions; Blow-up; NAVIER-STOKES EQUATIONS; UNIQUENESS THEOREM; EXISTENCE; SYSTEM;

D O I：

10.1007/s00013-011-0266-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using ideas arising in the works of LeJan and Sznitman and Mattingly and Sinai on their study of the Navier-Stokes equations, we investigate the blow-up behavior of a nonlinear parabolic equation subject to periodic boundary conditions.

引用

页码：69 / 78

页数：10

共 12 条

[1]

ANGENENT S, 1991, J DIFFER GEOM, V33, P601

[2] SOME ELEMENTARY ESTIMATES FOR THE NAVIER-STOKES SYSTEM [J].

Cortissoz, Jean .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (10) :3343-3353

[3]

FRIEDMAN A, 1986, ARCH RATION MECH AN, V96, P55

[4]

GAGE M, 1986, J DIFFER GEOM, V23, P69

[5]

Hamilton RS., 1988, Contemp. Math, V71, P237, DOI [DOI 10.1090/CONM/071/954419, 10.1090/conm/071/954419]

[6]

LeJan Y, 1997, PROBAB THEORY REL, V109, P343

[7] An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations [J].

Mattingly, JC ;

Sinai, YG .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 1999, 1 (04) :497-516

[8]

PASSO RD, 1987, J DIFFER EQUATIONS, V69, P1, DOI 10.1016/0022-0396(87)90099-4

[9]

Sinai YG, 2008, PURE APPL MATH Q, V4, P71

[10] Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source [J].

Souplet, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 153 (02) :374-406

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