Variational and Semigroup Methods for Waves and Diffusion in Networks
Abstract
We study diffusion and wave equations in networks. Combining semigroup and variational methods we obtain wellposedness and many nice properties of the solutions in general L^p context. Following earlier articles of other authors, we discuss how the spectrum of the generator can be connected to the structure of the network. We conclude by describing asymptotic behavior of solutions to the diffusion problem.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 DOI:
 10.48550/arXiv.1209.1495
 arXiv:
 arXiv:1209.1495
 Bibcode:
 2012arXiv1209.1495K
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Combinatorics;
 34B45;
 47D06;
 47D09
 EPrint:
 Appl. Math. Opt. (55) 2007, pages 219240