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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.

35A20 Analyticity in context of PDEs
35C10 Series solutions to PDEs
35G20 Nonlinear higher-order PDEs
Full Text: DOI
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