Pith Number

pith:W7V2X572

pith:2026:W7V2X572GQXM7GGHPUPW5PSRRB

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From Polynomial Stability to Periodic Well-posedness in Partially Dissipative Systems

Boris Muha, Giovanni P. Galdi, Justin T. Webster

Polynomial stability of the semigroup yields an explicit characterization of the dense forcing set on which periodic well-posedness holds via resolvent bounds that dictate required losses of time derivatives on the forcing.

arxiv:2605.12892 v1 · 2026-05-13 · math.AP · math.DS

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Claims

C1strongest claim

Polynomial stability of the semigroup yields an explicit characterization of the dense forcing set on which periodic well-posedness holds; resolvent bounds translate directly into certain losses of time derivatives on the forcing required to ensure well-posedness.

C2weakest assumption

The systems admit a Fourier decomposition in Hilbert space that converts polynomial decay rates into explicit resolvent bounds controlling the forcing class.

C3one line summary

Polynomial semigroup stability implies periodic well-posedness on a dense set of forcings whose time-derivative loss is controlled by resolvent bounds.

References

22 extracted · 22 resolved · 0 Pith anchors

[1] G. P. Galdi, M. Mohebbi, R. Zakerzadeh, P. Zunino, Hyperbolic–parabolic coupling and the occurrence of resonance in partially dissipative systems, in: Fluid-Structure Interaction and Biomedical Applic 2014

[2] I. Straˇ skraba, O. Vejvoda, Periodic solutions to abstract differential equations, Czechoslovak Math. J. 23 (1973) 635–669 1973

[3] Haraux, Non-resonance for a strongly dissipative wave equation in higher dimensions, Manuscripta Math 1985

[4] A. Borichev, Y. Tomilov, Optimal polynomial decay of functions and operator semigroups, Math. Ann. 347 (2010) 455–478 2010

[5] Pr¨ uss, On the spectrum ofC 0-semigroups, Trans 1984

Receipt and verification

First computed	2026-05-18T03:09:10.898311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7ebabf7fa342ecf98c77d1f6ebe518874427a0f3a159c5a42bed0a8eb0a7992

Aliases

arxiv: 2605.12892 · arxiv_version: 2605.12892v1 · doi: 10.48550/arxiv.2605.12892 · pith_short_12: W7V2X572GQXM · pith_short_16: W7V2X572GQXM7GGH · pith_short_8: W7V2X572

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W7V2X572GQXM7GGHPUPW5PSRRB \
  | 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: b7ebabf7fa342ecf98c77d1f6ebe518874427a0f3a159c5a42bed0a8eb0a7992

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "716b76edd22d69b9f1edcba4991296befb3ea40cc4503c01c3c81fc64814c94e",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T02:15:15Z",
    "title_canon_sha256": "6e7ec7159322508a4d6186812d8f99c1105d3a21daaed8c85ca74e82304aa80c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12892",
    "kind": "arxiv",
    "version": 1
  }
}