Physical applications of reciprocal transformations. (English) Zbl 0761.76086
Symmetries and nonlinear phenomena, Proc. Int. Sch. Appl. Math., Paipa/ Colomb. 1988, CIF Ser. 9, 260-288 (1988).
Summary: [For the entire collection see Zbl 0747.00041.]
A review is presented of the diversity of applications of reciprocal transformations to physical models. The provenance of such transformations is traced to early work on invariant transformations in gasdynamics. A reciprocal invariance theorem is presented, and an extension of an involutory gasdynamic invariance property to an orthogonal magneto-gasdynamic system is noted. The application of reciprocal transformations to the solution of boundary value problems is illustrated both by a Stefan problem in nonlinear heat conduction and a wave propagation problem in nonlinear visco-elasticity. The article concludes with a summary of other physical applications of reciprocal transformations.
A review is presented of the diversity of applications of reciprocal transformations to physical models. The provenance of such transformations is traced to early work on invariant transformations in gasdynamics. A reciprocal invariance theorem is presented, and an extension of an involutory gasdynamic invariance property to an orthogonal magneto-gasdynamic system is noted. The application of reciprocal transformations to the solution of boundary value problems is illustrated both by a Stefan problem in nonlinear heat conduction and a wave propagation problem in nonlinear visco-elasticity. The article concludes with a summary of other physical applications of reciprocal transformations.
MSC:
| 76N15 | Gas dynamics (general theory) |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 74Hxx | Dynamical problems in solid mechanics |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
