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 one-dimensional 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, Pelloni, and Sheils, 2014, for heat conduction on a series of one-dimensional rods connected end-to-end to the case of general configurations.

21 pages, 8 figures

References in corpus (3)

• Non-steady state heat conduction in composite walls
• Interface Problems for Dispersive equations
• Well-posedness and conditioning of 3rd and higher order two-point initial-boundary value problems

Cited by in corpus (5)

• The Linear KdV Equation with an Interface
• Wave scattering in 1D: D'Alembert-type representations and a reconstruction method
• Well-Posedness of Initial-Boundary Value Problems for a Reaction-Diffusion Equation
• Boundary value problems for evolution partial differential equations with discontinuous data
• Multilayer diffusion in a composite medium with imperfect contact