Singular Perturbation of Initial-Boundary Value Problems for a Class of Reaction Diffusion Systems

Mo Jia-qi

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Mo Jia-qi. Singular Perturbation of Initial-Boundary Value Problems for a Class of Reaction Diffusion Systems[J]. Applied Mathematics and Mechanics, 1991, 12(4): 375-384.

Citation:

Mo Jia-qi. Singular Perturbation of Initial-Boundary Value Problems for a Class of Reaction Diffusion Systems[J]. Applied Mathematics and Mechanics, 1991, 12(4): 375-384.

Citation:

Mo Jia-qi. Singular Perturbation of Initial-Boundary Value Problems for a Class of Reaction Diffusion Systems[J]. Applied Mathematics and Mechanics, 1991, 12(4): 375-384.

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Singular Perturbation of Initial-Boundary Value Problems for a Class of Reaction Diffusion Systems

Mo Jia-qi

Anhui Normal University, Wuhu

Received Date: 1990-01-19
Publish Date: 1991-04-15

Abstract

Abstract

In this paper,a class of singularly perturbed initial-boundary value problems for the reaction diffusion systems is considered.Using the theory of differential inequality,we prove that the initial-boundary value problems have a solution and obtain their asymptotic expansion.
- reaction diffusion system,
- singular perturbation,
- comparison theorem,
- asymptotic expansion

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References(13)

References

[1]	Carpenter,G.A.,A geometric approach to singular perturbation problem with application to nerve impulse equations,J.Diff.Eqs.,23,3(1977),335-367.
[2]	Williams,S.A.and P.L.Chow,Nonlinear reaction-diffusion models for interacting populations,J.Math.Appl.,62(1978),157-169.
[3]	Harada,K.and T.Fukao,Coexistence of competing species over a linear habitat of finite length,Math.Biosci.,38(1978),279-291.
[4]	Fife,P.C.,Pattern formation in reacting and diffusing systems,J.Chem.Phys.,64(1976),554-564.
[5]	Tyson,J.J.and P.C.Fife,Target pattern in a realistic model of the Belousov-Zhabotinskii reaction,J.Chem.Phys.,73(1980),2224-2237.
[6]	Nayfeh,A.H.,Introduction to Perturbation Techniques,John Wiley & Sons,New York(1981).
[7]	Howes,F.A.,The asymptotic solution of a class of singularly Perturbed nonlinear boundary value problems via differential inequalities,SIAM J.Math.Anal,9(1978),215-249.
[8]	Lakshmikantham,V.and R.Vaughn,Reaction-diffusion inequalites in cones,J.Math.Anal.Appl.,70(1979),1-9.
[9]	Pao,C.V.,Coexistence and stability of a competition-diffusion system in population dynamics,J.Math.Appl.,83(1981),54-76.
[10]	Mo Jia-qi(莫嘉琪),Singular perturbation for a boundary value problem of fourth order nonlinear differential equation,Chin,Ann.of Math.,8B(1987),80-88.
[11]	莫嘉琪,一类非线性反应-扩散方程组的奇摄动,中国科学,A辑,10(1988),1041-1049.
[12]	莫嘉琪,一类半线性椭圆型方程Dirichlet问题的奇摄动,数学物理学报,7(1987),395-401.
[13]	莫嘉琪,非线性向量微分方程初值问题的奇摄动,应用数学学报,12(1989),397-402.