Initial value problem for the dynamic system of anisotropic elasticity

A new method of solving equations of elasticity in inhomogeneous quasicrystals by means of symmetric hyperbolic systems

“…Applying the theory and methods of symmetric hyperbolic systems, we have proved that this model satisfies the Hadamard's correctness requirements: solvability, uniqueness, and stability with respect to perturbation of data. We note that the reduction of dynamic equations of classical anisotropic elasticity and magneto‐electro‐elasticity to the symmetric hyperbolic system and the study the Hadamards correctness requirements have been done before in Yakhno and Akmaz 30,33 . Moreover, in the present paper, a new analytical method of solving the initial value problem for the obtained symmetric hyperbolic system, which models the wave propagation in vertical inhomogeneous QCs, was developed.…”

“…The dynamic equations with the function coefficients for the classical elasticity, describing wave propagation in inhomogeneous anisotropic bodies, have been studied now quite well. These studies include such theoretical aspects as existence, uniqueness, and stability of solutions of initial and initial boundary value problems (see, for example, previous studies 27–32 ) as well as applications of these problems. We note that dynamic equations of 3‐D elasticity for QCs are more complicated than those of classical anisotropic elasticity.…”

A polynomial approach to determine the time-dependent electric and magnetic fields in anisotropic materials by symbolic computations

“…A new method, called the polynomial solution (PS) method, has been presented in Yakhno and Akmaz (2005) for the computation of the solution of the initial value 1180 COMPEL 35,3 problem of the system of anisotropic elasticity. The initial data and inhomogeneous term of the system of linear anisotropic elasticity has been considered as polynomials with respect to variables x 1 and x 2 .…”

An analytic solution of initial boundary value problem for 3D quasicrystals in half space

“…Following the idea suggested in [34][35][36], the solution method of the problem for elastodynamic model of quasicrystals, the model based on Bak's arguments, with polynomial data is established. In Section 2, basic equations of elastodynamic theory of quasicrystals and formulation of the problem are introduced.…”