Pith Number

pith:IIJSW6EJ

pith:2026:IIJSW6EJUVMJ2I2OWLVQZJY7IZ

not attested not anchored not stored refs resolved

On scalar nonlinear balance laws with singular nonlocal sources

Evangelia Ftaka, Khai T. Nguyen

Scalar nonlinear balance laws with singular nonlocal sources admit global entropy weak solutions in L2 under convexity and kernel conditions.

arxiv:2605.17422 v1 · 2026-05-17 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IIJSW6EJUVMJ2I2OWLVQZJY7IZ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in L²(ℝ), together with two partial uniqueness results, in the L²-periodic setting and non-periodic setting with L¹(ℝ) kernel.

C2weakest assumption

The convexity assumptions on the flux function and the specific regularity or positivity conditions imposed on the singular kernel (invoked in the abstract to obtain global existence and the Oleinik-type estimate).

C3one line summary

Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] F. Ancona, O. Glass, K. T. Nguyen, Lower compactness estimates for scalar balance laws,Comm. Pure Appl. Math.65(2012), 1303-1329–336 2012

[2] J. Biello and J. K. Hunter, Nonlinear Hamiltonian waves with constant frequency and surface waves on vorticity discontinuities,Comm. Pure Appl. Math.63(2009), 303–336 2009

[3] L. Bociu, E. Ftaka, K. T. Nguyen, J. Schino, Piecewise regular solutions to scalar balance laws with singular source terms,Journal of Differential Equations,409(2024), 181–222 2024

[4] Bressan,Hyperbolic Systems of Conservation Laws 2000

[5] A. Bressan and K. T. Nguyen, Global existence of weak solutions for the Burgers-Hilbert equation.SIAM Journal on Mathematical Analysis.46(2014), 2884–2904 2014

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:57.684689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42132b7889a5589d234eb2eb0ca71f464e4116085dec3c31f17e026da50601f6

Aliases

arxiv: 2605.17422 · arxiv_version: 2605.17422v1 · doi: 10.48550/arxiv.2605.17422 · pith_short_12: IIJSW6EJUVMJ · pith_short_16: IIJSW6EJUVMJ2I2O · pith_short_8: IIJSW6EJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IIJSW6EJUVMJ2I2OWLVQZJY7IZ \
  | 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: 42132b7889a5589d234eb2eb0ca71f464e4116085dec3c31f17e026da50601f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "477a05728390e145ef744c0e706de3c7b45cec11e05a8f2b954d6739d007e1a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-17T12:37:06Z",
    "title_canon_sha256": "56856f8db2b6681545cb6637f539ef0a168b0fa0426e9b29243092dbd014413e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17422",
    "kind": "arxiv",
    "version": 1
  }
}