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On the Cauchy problem for differential equations in spaces of resurgent functions. (English. Russian original) Zbl 0804.35019
Russ. Acad. Sci., Izv., Math. 40, No. 1, 67-94 (1993); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 56, No. 1, 75-104 (1992).
Summary: A new method is presented for finding asymptotic expansions of solutions of Cauchy problems of a wide class of equations of the type $\left[ - {\partial^ m \over \partial t \partial \xi^{m - 1}} + H \left( x, - {\partial \over \partial x}, {\partial \over \partial\xi} \right) \right] u(x,t,\xi) = 0, \quad x \in \mathbb{C}^ n,\;t \in \mathbb{C},\;\xi \in \mathbb{C},$ where $$H(x, \cdot, \cdot)$$ is a polynomial of order $$m$$. The method takes into consideration subdominant (i.e. exponentially small) terms, and it is based on the study of problems in special spaces of resurgent multivalued analytic functions.
##### MSC:
 35C20 Asymptotic expansions of solutions to PDEs 35G25 Initial value problems for nonlinear higher-order PDEs
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