English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider a diffusion process on the edges of a finite network and allowfor feedback effects between different, possibly non-adjacent edges. Thisgeneralizes the setting that is common in the literature, where the onlyconsidered interactions take place at the boundary, i. e., in the nodes of thenetwork. We discuss well-posedness of the associated initial value problem aswell as contractivity and positivity properties of its solutions. Finally, wediscuss qualitative properties that can be formulated in terms of invariance oflinear subspaces of the state space, i. e., of symmetries of the associatedphysical system. Applications to a neurobiological model as well as to a systemof linear Schroedinger equations on a quantum graph are discussed.

Well-Posedness and Symmetries of Strongly Coupled Network Equations