Heat equation on a network using the Fokas method
Abstract
The problem of heat conduction on networks of multiply connected rods is solved by providing an explicit solution of the onedimensional heat equation in each domain. The size and connectivity of the rods is known, but neither temperature nor heat flux are prescribed at the interface. Instead, the physical assumptions of continuity at the interfaces are the only conditions imposed. This work generalizes that of Deconinck et al (Proc. R. Soc. A 470 22) for heat conduction on a series of onedimensional rods connected endtoend to the case of general configurations.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 2015
 DOI:
 10.1088/17518113/48/33/335001
 arXiv:
 arXiv:1503.05228
 Bibcode:
 2015JPhA...48G5001S
 Keywords:

 Mathematics  Analysis of PDEs;
 35C15 (primary);
 35K05;
 35K20 (secondary)
 EPrint:
 21 pages, 8 figures