The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuity at the interface is imposed.
Bibliographical noteFunding Information:
The authors thank Peter Olver for useful discussions. This work was generously supported by the National Science Foundation under grant NSF-DMS-1008001 (B.D.). N.E.S. acknowledges support from the National Science Foundation under grant number NSF-DGE-0718124 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding sources.
- Heat equation
- Method of Fokas
- Periodic boundary conditions