On the solvability of fourth-order boundary value problems with accretive operators

Mohammed Benharrat (1) , Fairouz Bouchelaghem (2) , Alexandre Thorel (3)

1 ENPO-MA - École Nationale Polytechnique d'Oran Maurice Audin
2 Université d'Oran 1 Ahmed Ben Bella [Oran]
3 LMAH - Laboratoire de Mathématiques Appliquées du Havre

In this paper, we consider an abstract fourth order boundary value problem where the coefficients are accretive operators in Hilbert space. We show existence, uniqueness and maximal regularity of the solution under some necessary and sufficient conditions on the data. To this end, we give an explicit representation formula, using analytic semigroups, sectorial operators with Bounded Imaginary Powers, the theory of strongly continuous cosine operator functions and the perturbation theory of m-accretive operators. Illustrative example is also given.

Mots clés: Boundary value problems; accretive operators; analytic semigroup of contraction; cosine operator functions; maximal regularity

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Mohammed Benharrat, Fairouz Bouchelaghem, Alexandre Thorel. On the solvability of fourth-order boundary value problems with accretive operators. Semigroup Forum, In press, ⟨10.1007/s00233-023-10365-y⟩. ⟨hal-03226305v2⟩