Interaction between structures and bilinear fluids

Abstract As a mathematical model of fluids in which cavitation may occur, wave propagation in bilinear fluids is investigated. The principal difficulty is the determination of the a priori unknown and moving boundaries between the two stages of the fluid. A characteristic approach is used to study one-dimensional problems. Even in such relatively simple situations a considerable variety of cases may occur and a lengthy analysis is required. The paper discusses also the non-trivial questions of uniqueness and existence of solutions for the bilinear model. The procedure developed is applied to a typical example.