Nonlinear equations of the dynamics of an elastic micropolar medium. (English. Russian original) Zbl 0593.73019
J. Appl. Math. Mech. 48(1985), 291-299 (1984); translation from Prikl. Mat. Mekh. 48, 404-413 (1984).
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.
Reviewer: V.Gheorghiţă (Iaşi)
MSC:
| 74B20 | Nonlinear elasticity |
| 74G30 | Uniqueness of solutions of equilibrium problems in solid mechanics |
| 74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
| 74A99 | Generalities, axiomatics, foundations of continuum mechanics of solids |
| 74A35 | Polar materials |
Keywords:
reduced to symmetric form; condition of convexity of elastic; potential; transport equation; rate of change of weak discontinuity; along bicharacteristic; dynamics; elastic micropolar medium; hyperbolicity; compatibility conditions; strain; velocity fields; complete set of equations; system of local conservation laws; velocities of propagation of characteristic surfaces; estimate; growth of solutions; Cauchy problemReferences:
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