两个复时间变量初值问题的边界层展开
Boundary layer expansions for initial value problems with two complex time variables
摘要：
研究了复域上一类偏微分方程在复扰动参数$ε$作用下的解的存在性.我们构建内部和外部的解决方案的问题，并将它们与渐近表示通过Gevrey渐近展开$ε$，在适当的域。这种分析解的构造与[J. Mozo-Fernández，R. Schäfke，关于解析芽的渐近展开和可求和性，Publ. Math. 63（2019），no. 1，3- 79.]，而渐近表示依赖于由Ramis-Sibuya定理确定的上同调方法。
英文摘要：
We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter $ε$. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to $ε$, in adequate domains. The construction of such analytic solutions is closely related to the procedure of summation with respect to an analytic germ, put forward in[J. Mozo-Fernández, R. Schäfke, Asymptotic expansions and summability with respect to an analytic germ, Publ. Math. 63 (2019), no. 1, 3--79.], whilst the asymptotic representation leans on the cohomological approach determined by Ramis-Sibuya Theorem.
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