Nonlinear system of singular partial differential equations

Patrice Pongérard (1)

1 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT

This paper explores some nonlinear systems of singular partial differential equations written in the form t A D t U = Λ(t, x)U + f t, x, ζU, t A D x U. Under an assumption on Λ, unique solvability theorems are provided in the space of functions that are holomorphic in x on an open set, differentiable with respect to t on a real interval ]0, r] and extending to a continuous function at t = 0. The studied systems contain Fuchsian systems.

Mots clés: Nonlinear system; singular PDE; partially holomorphic functions

Domaines: Equations aux dérivées partielles [math.AP]

Patrice Pongérard. Nonlinear system of singular partial differential equations. Journal of Mathematical Sciences: Advances and Applications, 2017, 43 (1), pp.31-53. ⟨10.18642/jmsaa_7100121748⟩. ⟨hal-01465676⟩