Solvability of a transmission problem in Lp-spaces with generalized diffusion equation

Alexandre Thorel (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

We study a transmission problem, in population dynamics, between two juxtaposed habitats. In each habitat, we consider a generalized diffusion equation composed by the Laplace operator and a biharmonic term. We consider that the coefficients in front of each term could be negative or null. Using semigroups theory and functional calculus, we give some relation between coefficients to obtain the existence and the uniqueness of the classical solution in Lp-spaces.

Mots clés: Analytic semigroups; functional calculus; generalized diffusion equation; population dynamics; transmission problem

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

Alexandre Thorel. Solvability of a transmission problem in Lp-spaces with generalized diffusion equation. 2020. ⟨hal-02975666⟩