New Variation of Constants Formula for Some Partial Functional Differential Equations with Infinite Delay

Mostafa Adimy (1, 2) , Khalil Ezzinbi (3) , Aziz Ouhinou (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics
3 Département de mathématiques [FSSM]

In this work, we give a new variation of constants formula for some partial functional differential equations with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the known Hille-Yosida condition. When the phase space is a uniform fading memory space, we establish a spectral decomposition of the phase space. This allows us to study the existence of almost periodic solutions when the equation has a bounded solution on the half line $\mathbb{R}^+$

Mots clés: Hille-Yosida operator; integral solutions; variation of constants formula; uniform fading memory space; almost periodic solutions

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

Mostafa Adimy, Khalil Ezzinbi, Aziz Ouhinou. New Variation of Constants Formula for Some Partial Functional Differential Equations with Infinite Delay. 2006. ⟨hal-00258402⟩