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pith:6MJVSE6J

pith:2026:6MJVSE6JHT5ESPDZMPJ7CCFTMO

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The "good" Boussinesq equation on the half-line with Robin boundary conditions

Dionyssios Mantzavinos, Shivani Agarwal

The good Boussinesq equation on the half-line is locally well-posed in the Hadamard sense with nonzero Robin boundary conditions.

arxiv:2605.14335 v1 · 2026-05-14 · math.AP

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Claims

C1strongest claim

We prove the local Hadamard well-posedness of the ``good'' Boussinesq equation formulated on the half-line with nonzero Robin boundary conditions.

C2weakest assumption

The nonlinear analysis crucially relies on the linear estimates established through the explicit solution formula obtained for the forced linear counterpart of the problem via Fokas's unified transform.

C3one line summary

Local Hadamard well-posedness is proved for the good Boussinesq equation on the half-line with nonzero Robin boundary conditions, with solutions in Sobolev spaces that depend continuously on initial and boundary data.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] [AM ¨O24] A. Alkin, D. Mantzavinos, and T. ¨Ozsarı,Local well-posedness of the higher-order nonlinear Schr¨ odinger equation on the half-line: Single-boundary condition case, Studies in Applied Mathem 2024

[2] Dynamical Systems and Complexity 1988

[3] Cavalcante,The initial boundary value problem for some quadratic nonlinear Schr¨ odinger equations on the half-line, Differential Integral Equations30(2017), no 2017

[4] [Fam24] A. V. Faminskii,Global weak solutions of an initial-boundary value problem on a half-line for the higher order nonlinear Schr¨ odinger equation, J. Math. Anal. Appl.533(2024), no. 2, Paper No. 2024

[5] [Far09] L. G. Farah,Local solutions in Sobolev spaces with negative indices for the “good” Boussinesq equation, Comm. Partial Differential Equations34(2009), no. 1-3, 52–73. [FHM16] A. S. Fokas, A. A. 2009

Receipt and verification

First computed	2026-05-17T23:39:08.245210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3135913c93cfa493c7963d3f108b36381cbe26a516db32de81e4ad27874af86

Aliases

arxiv: 2605.14335 · arxiv_version: 2605.14335v1 · doi: 10.48550/arxiv.2605.14335

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6MJVSE6JHT5ESPDZMPJ7CCFTMO \
  | 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: f3135913c93cfa493c7963d3f108b36381cbe26a516db32de81e4ad27874af86

Canonical record JSON

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    "primary_cat": "math.AP",
    "submitted_at": "2026-05-14T03:59:40Z",
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