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Some Blow up Results of Nonlinear Parabolic Equation(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1999年04期
Page:
374-377
Research Field:
Publishing date:

Info

Title:
Some Blow up Results of Nonlinear Parabolic Equation
Author(s):
DingJianzhong
School of Sciences,NUST,Nanjing 210094
Keywords:
non-linear parabolic equat ions solution of equat ion blow-up
PACS:
O241.7
DOI:
-
Abstract:
This paper is concerned with the blow-up behavior of the solut ion of init ia-l boundary value problem for nonlinear parabolic equation w ith a gradient term: ut - $u = | ý u | p- | ý u | q p ≥2, p > q > 0 and ut - $u = | ý u | p - | u | q p≥2, 0 < q < 2. Using Poincare. s inequality and method of eigenfunct ion, it is proved that the solution of nonlinear parabolic equat ion blow s up in a finite t ime, provided init ial value is suitably large. New techniques are used in the proof, and Bebernes. results are extended.

References:

1 Chipot M,Weissler F B. Some blow-up results fo r a nonlinear par abolic equation w ith a greatient term. SIAM J Mat h Anal, 1989, 20: 886~ 907
2 Kaw olh B, Peletier L A. Obserations on blow- up and dead cores fo r nonlinear parabolic equations.Math Z, 1989, 202: 207~ 217
3 Bebernes J, Eber ly D. Char acterization of blow- up for a semilinear heat equation w ith a convect ion term. Mech Appl Math, 1989, 42( 3) : 447~ 456
4 Smoller J. Shock Wav es and React ion Diffusion Equations. New York: Spr ing er , 1983. 231~ 234
5 丁建中.Act ivator- inhibitor 模型的古典整体解.华东工学院学报, 1992, 16( 3) : 81~ 85

Memo

Memo:
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Last Update: 2013-03-29