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arXiv · 1912.03297

Higher order operators on networks: hyperbolic and parabolic theory

Federica Gregorio·Delio Mugnolo
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Abstract

We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations driven by this class of operators. We observe that they extend to the higher-order case and discuss well-posedness and conservation of energy of beam equations, along with regularizing properties of polyharmonic heat kernels. A noteworthy finding is the discovery of a new class of well-posed evolution equations with Wentzell-type boundary conditions.

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Federica Gregorio, Delio Mugnolo. 2019-12-06. Higher order operators on networks: hyperbolic and parabolic theory. https://doi.org/10.1007/s00020-020-02610-8

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