  In this work we study, by a semigroup approach, a transmission problem based
on biharmonic equations with boundary and transmission conditions, in two
juxtaposed habitats. We give a result of existence and uniqueness of the
classical solution in L p-spaces, for p $\in$ (1, +$\infty$), using analytic
semigroups and operators sum theory in Banach spaces. To this end, we invert
explicitly the determinant operator of the transmission system in L p-spaces
using the E $\infty$-calculus and the Dore-Venni sums theory.
