Alphabeta Math
TheoremStatement: Literature-sourcedProof: AI-generatedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06
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Uniqueness of a classical quasilinear solution before characteristic crossing

Statement

Let u,v∈C1 solve the same quasilinear Cauchy problem. On a connected region where their common characteristic projection from the data is a diffeomorphism, u=v.

Facts & Assumptions

Given: Two C1 solutions with identical data, and a connected region on which the common projection is a diffeomorphism.

Proof

technique · direct
1.1

The lifting lemma sends the restrictions of both solutions along each data-labelled characteristic to the same augmented initial-value problem.

givenconstruct
2.1

Uniqueness of that ODE gives equal lifted values u(X(s,y))=v(X(s,y)) on the strip.

step 1.1given
3.1

The diffeomorphic projection represents every point of the region as one X(s,y), so step 2.1 gives u=v there.

step 2.1given∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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