Uniqueness and continuous dependence for the equations of elastodynamics without strain energy function

DOI10.1007/BF00250626zbMath0273.73009MaRDI QIDQ2264566

Amy Cohen Murray

Publication date: 1972

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

Mathematics Subject Classification ID

Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Uniqueness of solutions of equilibrium problems in solid mechanics (74G30) Elastic materials (74B99)

Related Items

Nonexistence of global solutions in nonlinear Cauchy elastodynamics ⋮ Uniqueness and growth of weak solutions to certain linear differential equations in Hilbert space ⋮ Uniqueness and stability in linear viscoelasticity ⋮ A simplified two-fluid theory for helium II ⋮ Some new uniqueness and continuous dependence results for evolutionary equations of indefinite type: The weighted energy method ⋮ Some stability results in the linear theory of anisotropic elastodynamics ⋮ A stability theorem for a mixture of two viscous fluids at different temperatures ⋮ Growth and instability theorems for wave equations with dissipation, with applications in contemporary continuum mechanics ⋮ Classical elastodynamics as a linear symmetric hyperbolic system ⋮ Energy arguments in linear thermoelasticity ⋮ Continuous dependence for the compressible linearly viscous fluid ⋮ Improved Stability Estimates for Classes of Illposed Cauchy Problems

Cites Work

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• Uniqueness in classical elastodynamics
• The asymptotic behavior of solutions of second order systems of partial differential equations
• Continuous dependence on data for solutions of partial differential equations with a prescribed bound