Final answer:
The Gurtin-Pipkin or Coleman-Gurtin thermal law is used to couple the degenerate wave equation with the heat equation. This coupling allows for the study of heat transfer in materials that exhibit both wave-like and heat-like behavior.
Step-by-step explanation:
The Gurtin-Pipkin or Coleman-Gurtin thermal law is used to couple the degenerate wave equation with the heat equation via transmission. This coupling allows for the study of heat transfer in materials that exhibit both wave-like and heat-like behavior.
By incorporating the Gurtin-Pipkin or Coleman-Gurtin thermal law, the coupled equations describe how thermal energy is transferred between the wave-like motion and heat-like diffusion in the material.
For example, in the context of solids, the coupled equations can be used to study the propagation of phonons (wave-like vibrations) and thermal conduction simultaneously.