proposition 10.102 Jump form of the entropy inequality

open in the book · parts/02-mathematical-methods/08-pdes.tex:2655 · p. 368

Rests on

depends_on definition 10.101 Entropy pair; entropy inequality ¶
- depends_on definition 10.99 Entropy condition ¶
  - depends_on definition 10.95 Weak solution of a conservation law ¶
    - depends_on definition 10.93 Scalar conservation law ¶
      - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      - depends_on proposition 10.15 Method of characteristics, first order ¶
    - depends_on definition 10.83 Weak solution ¶
      - depends_on definition 17.38 Schwartz space and tempered distributions ¶
      - depends_on definition 10.3 Principal part and principal symbol ¶
  - depends_on theorem 10.96 Rankine–Hugoniot condition ¶
    - depends_on definition 10.95 Weak solution of a conservation law ¶ ↺
    - depends_on theorem 7.131 Green ¶
      - 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-77 ¶
    - proves proof ch:08-pdes@proof-40 ¶
- depends_on definition 10.95 Weak solution of a conservation law ¶ ↺
depends_on theorem 10.96 Rankine–Hugoniot condition ¶ ↺
proves proof ch:08-pdes@proof-41 ¶

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type	direction	node	provenance	where
`depends_on`	→	Entropy pair; entropy inequality	declared	parts/02-mathematical-methods/08-pdes.tex:2668
`depends_on`	→	Rankine–Hugoniot condition	declared	parts/02-mathematical-methods/08-pdes.tex:2668
`proves`	←	ch:08-pdes@proof-41	declared	parts/02-mathematical-methods/08-pdes.tex:2671