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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.
MSC:
35K05Heat equation
80A20Heat and mass transfer, heat flow
58J70Invariance and symmetry properties