Small effects in physics hinted by the Lie group philosophy: Are they observable? I: From Galilean principle to heat diffusion. (English) Zbl 0964.35508

Summary: The series of papers aimed to emphasize the role of the Lie group theoretic approach, as a fundamental principle for mathematical modeling. The subject of this first paper in the series is a discussion of the Galilean relativity principle in problems of linear heat conduction. It follows from the Galilean principle that the temperature changes under a change to different inertial coordinate frames. It is discussed how the invariance principle determines the linear heat equation and its fundamental solution.


35K05 Heat equation
80A20 Heat and mass transfer, heat flow (MSC2010)
58J70 Invariance and symmetry properties for PDEs on manifolds