Nonlinear equations of the dynamics of an elastic micropolar medium (Q1076539)

The purpose of the present paper is to study certain qualitative properties of the nonlinear equations of dynamics of an elastic micropolar medium that are associated with the concept of hyperbolicity. The compatibility conditions of the strain and velocity fields of simple structure are written and then the complete set of equations is represented as a system of local conservation laws. The velocities of propagation of characteristic surfaces are studied for the dynamic equations and the necessary condition for hyperbolicity is obtained from a constraint on the elastic potential function. Using the symmetric form of the nonlinear system of equations, the author formulates the sufficient condition for hyperbolicity. An estimate for the growth of solutions of the Cauchy problem and a uniqueness result are also obtained.