Special class of solutions of the kinetic equation of a bubbly fluid

Propagation of nonlinear waves in a rarefied bubbly flow

“…where f = f 1 . The class of solutions of the kinetic model ( 1) with a bounded support characterized by a linear relationship between the Riemann integral invariants was obtained in [9] on a base of the following property: if the functions f (t, x, p), p l (t, x), and p r (t, x) are a solution of system (1), (20) then the quantity R(t, x, p), which has been defined above by (19) in semi-Lagrangian coordinates, satisfies the equation…”

“…(µ and b are constants) leads to a special class of solutions [9]. In this case the distribution function f has the form…”

“…In [5], hyperbolicity conditions of the model are formulated and Riemann invariants and infinite series of conservation laws are found. The exact solutions of the Russo-Smereka kinetic equation in the classes of travelling and simple waves, as well as solutions with linearly dependent Riemann invariants, are obtained and studied in [8,9].…”