6533b7d3fe1ef96bd125ff3e
RESEARCH PRODUCT
Infinite lie groups of point transformations leaving invariant the linear equation which describes in the hodograph plane the isentropic one-dimensional gas flow
P. Carbonarosubject
Change of variables (PDE)HodographFlow (mathematics)Mechanics of MaterialsPlane (geometry)Applied MathematicsMechanical EngineeringMathematical analysisLie groupInvariant (mathematics)Linear equationSymmetry (physics)Mathematicsdescription
Abstract The group analysis of the hodograph equation which is equivalent to the non-linear system of one-dimensional isentropic gas dynamics reveals the existence of infinite groups of symmetry in correspondence with particular pressure laws. These turn out to be polytropes with selected indices, as is expected, as well as a new type of pressure. In all these cases the hodograph equation can be transformed, by a suitable change of variables, into the wave equationψ ζ = 0.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1991-01-01 | International Journal of Non-Linear Mechanics |