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4 papers · 2 filters
Variational and Semigroup Methods for Waves and Diffusion in Networks
Marjeta Kramar Fijavz, Delio Mugnolo, and Eszter Sikolya
We study diffusion and wave equations in networks. Combining semigroup and variational methods we obtain well-posedness and many nice properties of the solutions in general L^p -co…
Heat Kernel Bounds for the Laplacian on Metric Graphs of Polygonal Tilings
René Pröpper
We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as we…
Quantum graphs with mixed dynamics: the transport/diffusion case
Amru Hussein, Delio Mugnolo
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phen…
Regularity of Semigroups via the Asymptotic Behaviour at Zero
Stephan Fackler
An interesting result by T. Kato and A. Pazy says that a contractive semigroup (T(t)) on a uniformly convex space X is holomorphic iff limsup_{t \downarrow 0} ||T(t)-Id|| < 2. We s…