GEVREY PROPERTIES AND SUMMABILITY OF FORMAL POWER SERIES SOLUTIONS OF SOME INHOMOGENEOUS LINEAR CAUCHY-GOURSAT PROBLEMS

Pascal Remy (1)

1 LMV - Laboratoire de Mathématiques de Versailles

In this article, we investigate the Gevrey and summability properties of the formal power series solutions of some inhomogeneous linear Cauchy-Goursat problems with analytic coefficients in a neighborhood of $(0,0)\in\mathbb{C}^{2}$. In particular, we give necessary and sufficient conditions under which these solutions are convergent or are k-summable, for a convenient positive rational number k, in a given direction.

Mots clés: Linear partial differential equation; linear integro-differential equation; divergent power series; Newton polygon; Gevrey order; Gevrey asymptotic; summability

Domaines: Systèmes dynamiques [math.DS]; Equations aux dérivées partielles [math.AP]

Pascal Remy. GEVREY PROPERTIES AND SUMMABILITY OF FORMAL POWER SERIES SOLUTIONS OF SOME INHOMOGENEOUS LINEAR CAUCHY-GOURSAT PROBLEMS. 2018. ⟨hal-01778574⟩