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一类反应扩散方程组初值-边值问题的奇摄动

莫嘉琪

莫嘉琪. 一类反应扩散方程组初值-边值问题的奇摄动[J]. 应用数学和力学, 1991, 12(4): 375-384.
引用本文: 莫嘉琪. 一类反应扩散方程组初值-边值问题的奇摄动[J]. 应用数学和力学, 1991, 12(4): 375-384.
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.

一类反应扩散方程组初值-边值问题的奇摄动

基金项目: 国家自然科学基金

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

  • 摘要: 本文研究了一类反应扩散方程组的奇摄动初值一边值问题.利用微分不等式理论证明了该问题存在一个解并得到了其解的渐近展开式.
  • [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.
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出版历程
  • 收稿日期:  1990-01-19
  • 刊出日期:  1991-04-15

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