proposition A.159 The doubled inequality

open in the book · appendices/A-long-proofs.tex:8361 · p. 2869

Rests on

depends_on lemma A.157 Two elementary identities ¶
- depends_on definition A.150 Kruzhkov entropy pair ¶
  - depends_on definition 10.93 Scalar conservation law ¶
    - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      - depends_on definition 10.1 Partial differential equation; order ¶
    - depends_on proposition 10.15 Method of characteristics, first order ¶
      - depends_on definition 10.2 Linear, semilinear, quasilinear ¶ ↺
      - depends_on proposition 7.31 Chain rule ¶
      - proves proof ch:08-pdes@proof-5 ¶
  - 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 theorem 10.96 Rankine–Hugoniot condition ¶
    - depends_on definition 10.95 Weak solution of a conservation law ¶ ↺
- depends_on equation A.320 eq:app-kruzhkov-bounds ¶
- proves proof app:A-long-proofs@proof-93 ¶
depends_on proposition A.156 The Kruzhkov inequality ¶
- depends_on definition A.150 Kruzhkov entropy pair ¶ ↺
- depends_on definition 10.101 Entropy pair; entropy inequality ¶ ↺
- depends_on equation 10.92 eq:pde-entropy-inequality ¶
- proves proof app:A-long-proofs@proof-92 ¶
proves proof app:A-long-proofs@proof-94 ¶

Supports

depends_on proposition A.160 The cancellation ¶
- depends_on proposition A.162 The limit $\delta\to0$ ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Two elementary identities	declared	appendices/A-long-proofs.tex:8373
`depends_on`	→	The Kruzhkov inequality	declared	appendices/A-long-proofs.tex:8373
`depends_on`	←	The cancellation	declared	appendices/A-long-proofs.tex:8441
`proves`	←	app:A-long-proofs@proof-94	declared	appendices/A-long-proofs.tex:8376