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Disintegration conditions for a nonlinear wave in a viscoelastic medium. (English. Russian original) Zbl 0962.74030
Comput. Math. Math. Phys. 38, No. 2, 305-312 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 2, 315-323 (1998).
The authors study numerically quasi-transverse waves in a viscoelastic medium which interact with local inhomogeneities. The authors determine the parameters of inhomogeneities which can cause irreversible disintegration of a wave into a system of waves with different velocities. The corresponding initial-boundary value problem is approximated by nonlinear implicit finite difference scheme and solved first by Newton’s method, and then by the matrix sweep method.
MSC:
74J30 Nonlinear waves in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
74J40 Shocks and related discontinuities in solid mechanics
74D05 Linear constitutive equations for materials with memory
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