Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation

CAO Zhen-chao; CHEN Peng-nian

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CAO Zhen-chao, CHEN Peng-nian. Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1487-1492.

Citation:

CAO Zhen-chao, CHEN Peng-nian. Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1487-1492.

Citation:

CAO Zhen-chao, CHEN Peng-nian. Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1487-1492.

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Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation

CAO Zhen-chao¹,
CHEN Peng-nian²

1.
Department of Mathematics, Xiamen University, Xiamen, Fujian 361005, P. R. China;

Received Date: 2003-05-17
Rev Recd Date: 2005-05-31
Publish Date: 2005-12-15

Abstract

Abstract

For a class of nonlinear Filtration equation with nonlinear second-third boundary value condition,it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region.The priori estimate of the solutions was established by iterative method.By using this estimate the solutions may blow-upon the boundary of the region and thus it may have a symptotic non-stability.
- filtr ation equation,
- prior iestimate for the solution,
- asymptotic no n-stability,
- blow-up on the boundary

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References(8)

References

[1]	Rothe F.Uniform bounds from bounded L-functionals in reaction-diffusion equations[J].J Differential Equations,1982,45(2):207—233. doi: 10.1016/0022-0396(82)90067-5
[2]	Friedman A,Lacey A A.Blow up of solutions of semilinear parabolic equations[J].J Math Anal Appl,1988,132(1):171—186. doi: 10.1016/0022-247X(88)90052-2
[3]	Friedman A Mcleod B.Blow-up of positive solutions of semilinear heat equations[J].Indian Univ Math J,1985,34(2):425—447. doi: 10.1512/iumj.1985.34.34025
[4]	Gomez Lope J,Marquez V,Wolanski N.Blow-up results and localization of blow up points for the heat equation with a nonlinear boundary condition[J].J Differential Equations,1991,92(2):384—401. doi: 10.1016/0022-0396(91)90056-F
[5]	Alikakos N D.An application of the invariance principle to reaction-diffusion equations[J].J Differential Equations,1979,33(2):201—225. doi: 10.1016/0022-0396(79)90088-3
[6]	CAO Zhen-chao,GU Lian-kun.Initial-boundary value problem for a degenerate quasilinear parabolic equation of order 2m[J].J Partial Differential Equations,1990,3(1):13—20.
[7]	Ladyzenskaja O A,Solonnikov V A,Uralceva N N.Linear and Quasilinear Equations of Parabolic Type[M].AMS Translations of Mathematical Monographs,Vol 23,Rhode Island:AMS,1968.
[8]	Levin H A.Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time[J].J Differential Equations,1974,16(2):319—334. doi: 10.1016/0022-0396(74)90018-7