On Some Transmission Problems Set in a Biological Cell, Analysis and Resolution

Rabah Labbas (1) , Keddour Lemrabet (2) , Kheira Limam (3) , Ahmed Medeghri (3) , Maëlis Meisner (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 AMNEDP - Laboratoire AMNEDP, Faculté de Mathématiques, Université USTHB, Algérie
3 LMPA - Laboratoire de Mathématiques Pures et Appliquées

Some transmission problems are set in bodies with a crown of small thickness ε>0. For instance, those concerning the conductivity in the biological cell. By a natural change of variables, we transform them in transmission problems set in two cylindrical bodies ]−∞,0[×]−π,π[ and ]0,δ[×]−π,π[ (where δ=ln⁡(1+ε)) and then, in some general elliptic abstract differential equations (Pδ)δ>0. The goal of this work is to give a complete study of these problems(Pδ)δ>0 for every δ>0. Existence, uniqueness and maximal regularity results are obtained for the classical solutions essentially by using the semigroups theory.

Mots clés: Thin layers; Analytic semigroups; Transmission problems; Biological cells

Domaines: Equations aux dérivées partielles [math.AP]

Rabah Labbas, Keddour Lemrabet, Kheira Limam, Ahmed Medeghri, Maëlis Meisner. On Some Transmission Problems Set in a Biological Cell, Analysis and Resolution. Journal of Differential Equations, 2015, pp.In Press. ⟨10.1016/j.jde.2015.04.002⟩. ⟨hal-01138558⟩