Liviu Dinu
Institute of Mathematics of the Romanian Academy

Abstract. An analogue of the genuinely nonlinear character of an one-dimensional simple waves solution is identified and essentially used for 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-Ampere type representation] regarding their contribution to describing some nondegenerate gasdynamic [one-dimensional, multidimensional] regular interaction solutions. This is a joint paper with Marina-Ileana Dinu.