Pith Number

pith:RFSWKI2T

pith:2026:RFSWKI2TQ446BLSTPCS2VTIIWL

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Lifespan of Classical Solutions to One-Dimensional Quasilinear Wave Equations

Taro Yamanoi, Yuusuke Sugiyama

When the wave-speed derivative vanishes at zero, the lifespan of classical solutions to a one-dimensional quasilinear wave equation grows at least algebraically with the smallness of the initial data.

arxiv:2605.04976 v2 · 2026-05-06 · math.AP

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\pithnumber{RFSWKI2TQ446BLSTPCS2VTIIWL}

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Record completeness

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Our result shows that the lifespan of the solution extends algebraically depending on the smallness of the initial data. Furthermore, we also show that when c(θ) is flat at the origin, the lifespan extends exponentially depending on the smallness of the initial data.

C2weakest assumption

The derivative of c(θ) tends to 0 near the origin (or c is flat there), together with the implicit assumption that classical solutions exist up to the lifespan and that the method of characteristics applies without additional singularities.

C3one line summary

For this quasilinear wave equation with c'(θ) approaching zero at the origin, classical solution lifespan extends algebraically with small initial data and exponentially when c is flat at the origin.

Receipt and verification

First computed	2026-06-08T01:04:06.633067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89656523538739e0ae5378a5aacd08b2d2f634ac740f2d9e68ec4cb2e643e697

Aliases

arxiv: 2605.04976 · arxiv_version: 2605.04976v2 · doi: 10.48550/arxiv.2605.04976 · pith_short_12: RFSWKI2TQ446 · pith_short_16: RFSWKI2TQ446BLST · pith_short_8: RFSWKI2T

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RFSWKI2TQ446BLSTPCS2VTIIWL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 89656523538739e0ae5378a5aacd08b2d2f634ac740f2d9e68ec4cb2e643e697

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c3658ac924b89d988d789d7925af54b6a0fa4dc77e26bba0b7948f972471a78",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-06T14:31:38Z",
    "title_canon_sha256": "1087960bec2a9abcd5665b13658336687ff4960080e17899d6796b79887d5bb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04976",
    "kind": "arxiv",
    "version": 2
  }
}