Why the Colombeau Algebras Cannot Formulate, Let Alone Prove the Global Cauchy-Kovalevskaia Theorem ?

Elemer Elad Rosinger (1)

1 Department of Mathematics and Applied Mathematics [Pretoria]

It is briefly shown that, due to the growth conditions in their definition, the Colombeau algebras cannot handle arbitrary analytic nonlinear PDEs, and in particular, cannot allow the formulation, let alone, give the proof of the global Cauchy-Kovalevskaia theorem.

Mots clés: Colombeau algebras; failure to formulate and prove the global Cauchy-Kovalevskaia theorem

Domaines: Mathématiques générales [math.GM]; Equations aux dérivées partielles [math.AP]

Elemer Elad Rosinger. Why the Colombeau Algebras Cannot Formulate, Let Alone Prove the Global Cauchy-Kovalevskaia Theorem ?. 2011. ⟨hal-00590876⟩