Far Eastern Mathematical Journal

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The evolution equation of transverse shock waves in solids


Ragozina V. E., Ivanova Yu. E.

2013, issue 1, Ñ. 116-126


Abstract
Solution of a number of boundary value problems by the method of matched asymptotic expansions for single-wave processes in incompressible nonlinear elastic media is carried out. The frontal area of the wave is defined by the nonlinear evolution equation, which is different from the Cole – Hopf equation. This demonstrates the fundamental differences in the mechanisms of formation and subsequent movement of volume and shear shock waves. The authors propose the inclusion of particular solutions of the evolution equation in the additional parametric method for the determination of the displacement field and medium strains.

Keywords:
nonlinear elasticity, incompressibility, shock wave, perturbation method, evolution equation

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