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On the summability of the formal solutions for some PDEs with irregular singularity. (English. Abridged French version) Zbl 1028.35006
Summary: We consider some classes of nonlinear partial differential equations with regular singularity with respect to $$t= 0$$ and irregular one with respect to $$x= 0$$. Our purpose is to establish a result which is similar to the $$k$$-summability property, known in the case of singular ordinary differential equations. We can prove that, except at most a countable set, the formal solution is Borel summable or $$k$$-summable with respect to $$x$$ in all other directions.

##### MSC:
 35A20 Analyticity in context of PDEs 35C10 Series solutions to PDEs 35G20 Nonlinear higher-order PDEs
##### Keywords:
regular singularity; irregular singularity; formal solution
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##### References:
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