Well-Posedness and Symmetries of Strongly Coupled Network Equations

Details Well-Posedness and Symmetries of Strongly Coupled Network Equations Well-Posedness and Symmetries of Strongly Coupled Network Equations

2007-09-13

arxiv.org/abs/0709.2080v2

J. Phys. A 41 (2008), 055102

Mathematics

Functional Analysis

25 pages. Corrected typos and minor changes

Scientific paper

10.1088/1751-8113/41/5/055102

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

Affiliated with

Also associated with

No associations

Rating

Well-Posedness and Symmetries of Strongly Coupled Network Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Well-Posedness and Symmetries of Strongly Coupled Network Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-Posedness and Symmetries of Strongly Coupled Network Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215048