10 citations · 17 across the 17 of their papers we have counts for
5 papers · 1 filter
A Picard-Lindelöf theorem for smooth PDE
Paolo Giordano, Lorenzo Luperi Baglini
We prove that Picard-Lindelöf iterations for an arbitrary smooth normal Cauchy problem for PDE converge if we assume a suitable Weissinger-like sufficient condition. This condition…
Generalized solutions in PDE's and the Burgers' equation
Vieri Benci, Lorenzo Luperi Baglini
In many situations, the notion of function is not sufficient and it needs to be extended. A classical way to do this is to introduce the notion of weak solution; another approach i…
A generalization of Gauss' divergence theorem
Vieri Benci, Lorenzo Luperi Baglini
This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently…
Ultrafunctions and Applications
Vieri Benci, Lorenzo Luperi Baglini
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is th…
A model problem for ultrafunctions
Vieri Benci, Lorenzo Luperi Baglini
The purpose of this paper is to show that Non-Archimedean Mathematics (NAM), namely mathematics which uses infinite and infinitesimal numbers, is useful to model some Physical prob…