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

Ibragimov, Nail H.

Lie Groups Appl. 1, No. 1, 113-123 (1994).

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:

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

Keywords:

Galilean relativity principle; fundamental solution