[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()

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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

Author(s):

Yang Ming

Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

parabolic system;  degenerate;  global existence;  blow-up

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.

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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