Nonuniqueness for a hyperbolic system: cavitation in nonlinear elastodynamics

DOI10.1007/BF00251490zbMath0651.73005OpenAlexW1980377011MaRDI QIDQ1106677

Pericak-Spector, Kathleen A., Spector, Scott J.

Publication date: 1988

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251490

zbMATH Keywords

nonlinear elastodynamicsinitial boundary value problemadmissibility of the solutionsnontrivial (weak) solutionradial cavitation similarity solutions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Nonlinear elasticity (74B20) Fracture and damage (74R99) Initial value problems for second-order hyperbolic equations (35L15)

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Cites Work

• Discontinuous energy minimizers in nonlinear elastostatics: An example of J. Ball revisited
• A bifurcation problem for a compressible nonlinearly elastic medium: Growth of a micro-void
• Radially symmetric cavitation for hyperelastic materials
• Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity
• The propagation of phase boundaries in elastic bars
• The second law of thermodynamics and stability
• A uniqueness theorem for the displacement problem in finite elastodynamics
• Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type
• Admissibility criteria for propagating phase boundaries in a van der Waals fluid
• The entropy rate admissibility criterion for solutions of hyperbolic conservation laws
• Hyperbolic systems of conservation laws II
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity