proposition 10.94 Gradient catastrophe

open in the book · parts/02-mathematical-methods/08-pdes.tex:2467 · p. 366

Rests on

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 definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 6.2 Open set ¶
      - depends_on definition 6.1 Topological space ¶
- 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 ¶
    - depends_on definition 7.13 Composite function ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on proposition 7.27 Differentiable implies continuous ¶
      - depends_on definition 7.20 Continuity at a point ¶ ↺
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on proposition 7.6 Algebra of limits ¶
      - proves proof ch:05-real-analysis@proof-11 ¶
    - depends_on proposition 7.6 Algebra of limits ¶ ↺
    - proves proof ch:05-real-analysis@proof-15 ¶
  - proves proof ch:08-pdes@proof-5 ¶
depends_on proposition 10.15 Method of characteristics, first order ¶ ↺
proves proof ch:08-pdes@proof-39 ¶

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type	direction	node	provenance	where
`depends_on`	→	Scalar conservation law	declared	parts/02-mathematical-methods/08-pdes.tex:2479
`depends_on`	→	Method of characteristics, first order	declared	parts/02-mathematical-methods/08-pdes.tex:2479
`proves`	←	ch:08-pdes@proof-39	declared	parts/02-mathematical-methods/08-pdes.tex:2482