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The augmented characteristic system for a quasilinear first-order PDE
Definition
For the problem in Semilinear and quasilinear first-order Cauchy problems on a parametrised hypersurface, its augmented characteristic strip is a map satisfying
Here is the characteristic parameter and labels the initial point. The system concerns only ; no differential equation for a putative gradient is included in this definition.
Depends on
Used by
- Characteristic crossing and caustic for a first-order PDE Definition
- Semilinear characteristics with logistic growth Example
- A quasilinear solution lifts to augmented characteristics Lemma
- Jacobian of a characteristic strip at its initial surface Lemma
- Local solvability and C1 parameter dependence for the augmented characteristic ODE Lemma
- Local quasilinear characteristic graph construction Theorem
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- First order PDE: The Methods of Characteristics (standard reference, not scraped)