This work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows one to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work (Lastra and Malek in Adv. Differ. Equ. 2020:20, 2020) by the last two authors. The result leans on the application of a fixed point argument and the classical Ramis–Sibuya theorem.

中文翻译：

---

通过截断的拉普拉斯变换在两个复杂时间变量中的参数Gevrey渐近性

这项工作致力于研究复杂域中的偏微分方程的线性初始值问题，处理两个复杂的时间变量。在解析解决方案的构造中使用截断的类似拉普拉斯的变换，可以克服因几何问题而引起的小除数现象，并代表了最近工作中提出的一种替代方法（Lastra和Malek in Adv （两位作者，Differ。Equ。2020：20，2020）。结果取决于不动点参数和经典的Ramis–Sibuya定理的应用。