Pith Number

pith:3VGKUCOA

pith:2026:3VGKUCOA2HWKT4PYQCBKPJDO5M

not attested not anchored not stored refs resolved

Forward and inverse problems for a time-fractional pseudo-parabolic equation with variable coefficients

Elbek Husanov, Ravshan Ashurov

Global existence and uniqueness hold for the forward problem of a time-fractional pseudo-parabolic equation with time-dependent coefficient, and global existence holds for the associated inverse source problem.

arxiv:2605.13285 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

The global existence and uniqueness of the solution to the forward problem is proved for time-dependent σ(t), and the global existence of the solution to the inverse problem is proved by applying Schauder's fixed point theorem.

C2weakest assumption

The functional F is assumed to be such that the associated mapping satisfies the hypotheses of Schauder's fixed point theorem, and the operator A possesses a discrete spectrum of positive eigenvalues with the requisite regularity.

C3one line summary

Global existence and uniqueness are proved for the forward problem with variable σ(t) and for the inverse problem of recovering the source r(t) from a general overdetermination condition F[u(t)] = Φ(t).

References

17 extracted · 17 resolved · 0 Pith anchors

[1] Lizama,Abstract linear fractional evolution equations, inHandbook of Fractional Calculus with Applications, Vol 2019

[2] A. V. Pskhu,Fractional Differential Equations(Moscow, Russia, Nauka, 2005) 2005

[3] On a theory of heat conduction involving two temperatures, 1968

[4] Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, 1960

[5] Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data, 1980

Receipt and verification

First computed	2026-05-18T02:44:49.159593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd4caa09c0d1eca9f1f88082a7a46eeb26bb1f93acd9834ab359e526f984a52c

Aliases

arxiv: 2605.13285 · arxiv_version: 2605.13285v1 · doi: 10.48550/arxiv.2605.13285 · pith_short_12: 3VGKUCOA2HWK · pith_short_16: 3VGKUCOA2HWKT4PY · pith_short_8: 3VGKUCOA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3VGKUCOA2HWKT4PYQCBKPJDO5M \
  | 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: dd4caa09c0d1eca9f1f88082a7a46eeb26bb1f93acd9834ab359e526f984a52c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5862f941ba77ad7e8588e10c5b30764268581e000e3826af7af7459588640afc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T10:01:32Z",
    "title_canon_sha256": "20bd33e5f853fd0cf2f8884f80c19ac0f743c345eea972c7fd29464f06a022e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13285",
    "kind": "arxiv",
    "version": 1
  }
}