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The decay and formation of one-dimensional nonconservative shocks. (English) Zbl 0644.73033
The method of singular surfaces is used to obtain explicit conditions under which a one-dimensional acceleration wave develops into a shock when some dissipation mechanism is present. The conditions which secure the initial growth of the strong shock wave propagating into an undeformed nonlinear and dissipative medium are also derived. The analysis is presented for a single-balance law, one-dimensional elasticity, and the nonlinear Maxwellian continuum.
MSC:
74J99 Waves in solid mechanics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L67 Shocks and singularities for hyperbolic equations
74M20 Impact in solid mechanics
74B20 Nonlinear elasticity
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