theorem 30.42 Uniqueness in elastodynamics

Rests on

• depends_on proposition 30.41 Energy balance and its flux ¶
  • depends_on equation 30.23 eq:elast-energy-density ¶
  • depends_on theorem 30.40 Navier–Cauchy equations ¶
    • depends_on equation 30.21 eq:elast-hooke-isotropic ¶
    • depends_on theorem 30.21 Cauchy's equation of motion ¶
      • depends_on theorem 7.133 Gauss ¶
        • depends_on definition 7.127 Simple regions ¶
        • depends_on remark 7.128 What the derivations below take as given ¶
        • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • proves proof ch:05-real-analysis@proof-79 ¶
      • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
        • depends_on definition 30.17 Traction ¶
        • depends_on definition 13.5 Tensor under orthogonal transformations ¶
        • proves proof ch:13-continuum-elasticity@proof-7 ¶
      • proves proof ch:13-continuum-elasticity@proof-9 ¶
    • proves proof ch:13-continuum-elasticity@proof-18 ¶
  • proves proof ch:13-continuum-elasticity@proof-19 ¶
• depends_on proposition 30.30 Stability bounds ¶
  • depends_on equation 30.23 eq:elast-energy-density ¶ ↺
  • depends_on theorem 5.116 Sylvester's law of inertia ¶
    • depends_on definition 5.110 Bilinear map ¶
      • depends_on definition 5.37 Linear transformation ¶
        • depends_on definition 4.33 Vector space ¶
    • depends_on definition 5.111 Symmetric and antisymmetric forms ¶
      • depends_on definition 5.110 Bilinear map ¶ ↺
      • depends_on equation 5.137 eq:lin-bilinear-matrix ¶
    • depends_on equation 5.139 eq:lin-bilinear-congruence ¶
    • proves proof ch:03-linear-algebra-representations@proof-53 ¶
  • proves proof ch:13-continuum-elasticity@proof-13 ¶
• proves proof ch:13-continuum-elasticity@proof-20 ¶

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