【作者】 陈璐诗；

【导师】 李平丽；

【作者基本信息】 渤海大学 ， 基础数学， 2012， 硕士

【摘要】 20世纪以来，随着人们对于解析偏微分方程的发散级数解的研究以及对于这些发散级数解的意义的探索，经典的渐近展开及可和性理论得到了很好的发展，现在成为了应用背景更为广泛及研究前景更为广阔的Gevrey渐近展开理论及可和与多重可和理论。本文第一部分：通过比较系数法验证某一奇异偏微分方程存在唯一形式幂级数解，给出该级数解的具体形式，利用形式Borel变换证明此形式幂级数解关于某单项式是1-Gevrey的。第二部分：利用泛函分析中的不动点定理以及Gevrey渐近理论及可和理论中的部分结论证明上述形式解关于某单项式是1-可和的。更多还原

【Abstract】 Since the20th century, with the study on divergent power series solution and the exploringof the meaning of them, the classical asymptotic expansion theory and summability theory havebeen developed rapidly. And now they become Gevrey asymptotic expansion theory andmultisummability theory, which have more extansive used and wider vistas of research.Part one: We prove the existence and uniqueness of the formal power series solution to asingular partial differential equation by comparing coeffients of an identity, given the specificform of the series solution, we construct holomorphic solution of the problem with the help ofthe formal Borel transform, and prove that the formal power series solution is1-Gevrey.Part two: We use the fixed point theorem and part of the results in Gevrey asymptotictheory and summability theory to prove that the above formal solution is1-summable in amonomial.更多还原