Nondegeneracy, from the Prospect of Wave-wave Regular Interactions of a Gasdynamic Type : Some Remarks

An analogue of the genuinely nonlinear character of an one-dimensional simple waves solution is identified and essentially used in the construction of some multidimensional extensions (simple waves solutions, regular interactions of simple waves solutions). A class of exact multidimensional gasdynamic solutions is constructed whose interactive elements are regular. Some specific aspects of Burnat’s multidimensional “algebraic” description [which uses a dual connection between the hodograph and physical characteristic details] are identified and classified with an admissibility criterion − selecting a “genuinely nonlinear” type where other (“hybrid”) types are formally possible. A parallel is constructed between Burnat’s “algebraic” approach and Martin’s “differential” approach [centered on a Monge−Ampère type representation] regarding their contribution to describing some nondegenerate one-dimensional gasdynamic regular interaction solutions. The present approach parallels, from a local prospect, some details of the twodimensional global approach of [16]. Introduction. Burnat’s “algebraic” approach For the multidimensional first order hyperbolic system of a gasdynamic type [whose coefficients only depend on u] n ∑