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On the summability of formal solutions for a class of nonlinear singular PDEs with irregular singularity. (English) Zbl 1098.35006
Berhanu, Shiferaw (ed.) et al., Recent progress on some problems in several complex variables and partial differential equations. Papers presented at the international conferences on partial differential equations and several complex variables, Wuhan, China, June 9–13, 2004 and on complex geometry and related fields, Shanghai, China, June 21–24, 2004. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3921-7/pbk). Contemporary Mathematics 400, 53-64 (2006).
The authors consider summability problems for singular PDE in which the formal solutions are convergent for small $$t$$ but divergent for small $$x$$. The $$k$$-summability of these series has been proved.
For the entire collection see [Zbl 1086.32001].

##### MSC:
 35A20 Analyticity in context of PDEs 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35G20 Nonlinear higher-order PDEs