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A biharmonic transmission problem in Lp-spaces

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This research is supported by CIFRE contract 2014/1307 with Qualiom Eco company and partially by the LMAH and the european funding ERDF through grant project Xterm
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  • 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 $ \mathcal{E}_{\infty} $-calculus and the Dore-Venni sums theory.

    Mathematics Subject Classification: 35B65, 35J48, 35R20, 47A60, 47D06.


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