proposition 10.25 The backward heat problem is ill posed

Rests on

• depends_on definition 10.6 Type of a second-order operator ¶
  • depends_on definition 10.4 The second-order operator ¶
    • depends_on definition 10.3 Principal part and principal symbol ¶
      • depends_on definition 10.2 Linear, semilinear, quasilinear ¶
        • depends_on definition 10.1 Partial differential equation; order ¶
      • depends_on equation 10.2 eq:pde-multi-index ¶
    • depends_on proposition 7.105 Clairaut–Schwarz ¶
      • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.16 Limit ¶
        • depends_on equation 7.7 eq:ana-limit-left ¶
        • depends_on equation 7.5 eq:ana-limit-right ¶
      • depends_on theorem 7.35 Mean value theorem ¶
        • depends_on proposition 7.29 Linearity ¶
        • depends_on theorem 7.34 Rolle ¶
        • proves proof ch:05-real-analysis@proof-19 ¶
      • proves proof ch:05-real-analysis@proof-64 ¶
  • 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 ¶
• depends_on definition 10.24 Well-posed problem ¶
  • depends_on definition 10.1 Partial differential equation; order ¶ ↺
  • depends_on definition 6.24 Metric ¶
    • depends_on definition 3.43 Map ¶
      • depends_on definition 3.24 Quantifiers ¶
        • depends_on definition 3.23 Predicate ¶
      • depends_on definition 3.28 Set ¶
    • depends_on definition 3.38 Ordered pair and Cartesian product ¶
• proves proof ch:08-pdes@proof-8 ¶

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