[1] Yang Ming,. Global existence and blow up of a degenerate parabolic system [J]. Journal of Southeast University (English Edition), 2003, 19 (4): 427-431. [doi:10.3969/j.issn.1003-7985.2003.04.026]

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Global existence and blow up of a degenerate parabolic system()

一个退化抛物型方程组解的整体存在性与爆破

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 4

Page:

427-431

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-12-30

Info

Title:

Global existence and blow up of a degenerate parabolic system

一个退化抛物型方程组解的整体存在性与爆破

Author(s):

Yang Ming

Department of Mathematics, Southeast University, Nanjing 210096, China

杨明

东南大学数学系, 南京 210096

Keywords:

parabolic system;  degenerate;  global existence;  blow-up

抛物型方程组;  退化;  整体存在性;  爆破

PACS:

O175.26

DOI:

10.3969/j.issn.1003-7985.2003.04.026

Abstract:

This paper deals with positive solutions of a degenerate parabolic system:u_t=Δu^m+v^pln^α(h+u), v_t=Δvⁿ+u^qln^β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two-component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.

研究了一个具有齐次Dirichlet边界条件以及正的初值条件的退化抛物型方程组:u_t=Δu^m+v^pln^α(h+u), v_t=Δvⁿ+u^qln^β(h+v).该方程组描述了一个具有2种连续介质的燃烧过程及热扩散过程. 本文利用上、下解方法获得了方程组解的整体存在性和爆破的条件.

References:

[1] Andserson J R. Local existence and uniqueness of solutions of degenerate parabolic equations [J]. Commun in Partial Differential Equations, 1991, 16(1): 105-143.
[2] Rossi J D, Wolanski N. Blow-up versus global existence for a semilinear reaction diffusion system in a bounded domain [J]. Commun in Partial Differential Equations, 1995, 20(11, 12): 1991-2004.
[3] Escobedo M, Herro M A. Boundedness and blow-up for a semilinear reaction diffusion system [J]. J Differential Equation, 1991, 89:176-202.
[4] Mu C L, Su Y. Global existence and blow up for a quasilinear degenerate parabolic system in a cylinder [J]. Appl Math Letters, 2001, 14: 715-723.
[5] Samarskii A A, Galaktionov V A, Kurdyumov S P, et al. Blow up in problems for quasilinear parabolic equations [M]. Berlin: Walter de Gruyter, 1995.
[6] Wang M X. Note on a quasilinear parabolic system [J].Nonlinear Analysis(Theory Method and Applications), 1997, 29(7): 813-821.
[7] Wang M X. Global existence and finite time blow up for reaction-diffusion system [J]. Z Angew Math Phys, 2000, 51: 160-167.
[8] Lu W D. Variational methods in differential equations [M]. Chengdu: Press of Sichuan University, 1995. 217-218.(in Chinese)

Memo

Memo:

Biography: Yang Ming(1979—), male, associate professor, math-yangming@yahoo.com.cn.

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