具有多重解的非线性奇摄动问题

利用边界层法,研究了一类具有多重解的非线性奇摄动问题．在适当的假设下,通过给出外部解展开式系数及其对应边界条件的一般表达式,根据退化问题的边值作为某方程的根的重数,得到了此问题不同形式的渐近解．特别地,当这种根的重数为偶数时,问题具有二重解．另外,将相关结果应用于化学反应器理论,并通过对具有多重解的例子的渐近解和精确解的数值模拟说明如此构造的渐近解具有较高的精度．

Nonlinear Singularly Perturbed Problem With Multiple Solutions

In this paper,using the method of boundary layer,a nonlinear singularly perturbed problem with multiple solutions is studied.Under the appropriate assumptions, the asymptotic solutions of the problem with different forms are obtained according to the multiple number of the root of some equation,which is satisfied by the boundary value of the reduced problem,by giving the general expressions for the coefficients of outer solution expansion and the corresponding boundary conditions.In particular,as the multiple number of the root is even,the problem has two solutions.In addition,the relative result is applied into the theory of chemical reactors.And it is illustrated that the asymptotic solutions so constructed possess higher precision by simulating the asymptotic solutions and numerical solutions for an example with multiple solutions.