Chugainova A.P.
On solution non-uniqueness in the nonlinear elasticity theory
The simultaneous effects of dissipation and dispersion on nonlinear wave behavior in elastic media are considered when the effects are small and manifested only in narrow high-gradient regions. If one constructs solutions of self-similar problems in ``hyperbolic'' approximation using Riemann's waves and admissible discontinuities (i.e., discontinuities with structures) one obtains many solutions the number of which unlimitedly grows with growing the relative influence of dispersion (as compared to dissipation) in discontinuity structures.
The numerical analysis (based on PDE with dispersion and dissipation) of nonself-similar problems with self-similar asymptotics is performed to determine which of self-similar solutions is an asymptotic form for the nonself-similar solution.
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