Pith Number

pith:I7PLR6QB

pith:2025:I7PLR6QBVZMVCLHK3TJZBEEOIO

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Reconstruction of degeneracy region and power for parabolic equations and systems

Anna Doubova, Piermarco Cannarsa, Veronica Danesi

Sufficient initial data conditions guarantee unique and stable recovery of the degeneracy point from one boundary measurement in degenerate parabolic equations.

arxiv:2509.13962 v3 · 2025-09-17 · math.AP

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Claims

C1strongest claim

We derive sufficient conditions on the initial data that guarantee the stability and uniqueness of the solution obtained from a one-point measurement. Moreover, we present more general uniqueness theorems, which also cover the identification of the initial data, the coefficient of the zero order term and the degeneracy power, using measurements taken over time.

C2weakest assumption

The analysis assumes that the solution admits an explicit representation in terms of Bessel functions for the spectral problem associated with the degenerate diffusion operator, which is invoked to obtain the uniqueness and stability results.

C3one line summary

Sufficient conditions on initial data guarantee unique and stable reconstruction of the degeneracy point, power, and related coefficients in strongly degenerate 1D parabolic equations and systems from one-point or time-dependent boundary observations.

References

33 extracted · 33 resolved · 0 Pith anchors

[1] M. Abramowitz, I. A. Stegun. Handbook of Mathematical Funct ions with Formulas, Graphs, and Mathematical Tables. vol. 55, U. S. Government Printing Oﬃce, Washington (1964) 1964

[2] F. Alabau-Boussouira, P. Cannarsa, G. Fragnelli. Carleman estim ates for degenerate parabolic operators with applications to null controllability. J. Evol. Equ., 6 (20 06), pp. 161–204

[3] J. Apraiz, J. Cheng, A. Doubova, E. Fern´ andez-Cara, M. Yam amoto. Uniqueness and nu- merical reconstruction for inverse problems dealing with interval s ize search. Inverse Probl. Imaging 16 (2022) 2022

[4] F. Black, M. Scholes. The pricing of options and corporate liabilities . J. Polit. Econ. 81 (1973) 637–54 1973

[5] M. Campiti, G. Metafune, D. Pallara. Degenerate self-adjoint ev olution equations on the unit interval. Semigroup Forum, 57 (1998), pp. 1–36 1998

Formal links

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Receipt and verification

First computed	2026-06-19T16:12:47.788061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47deb8fa01ae59512ceadcd390908e43b8320f6958819e849350c84942b720a4

Aliases

arxiv: 2509.13962 · arxiv_version: 2509.13962v3 · doi: 10.48550/arxiv.2509.13962 · pith_short_12: I7PLR6QBVZMV · pith_short_16: I7PLR6QBVZMVCLHK · pith_short_8: I7PLR6QB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/I7PLR6QBVZMVCLHK3TJZBEEOIO \
  | 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: 47deb8fa01ae59512ceadcd390908e43b8320f6958819e849350c84942b720a4

Canonical record JSON

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    "abstract_canon_sha256": "7ddc21286cd5b11b75cbd5b8ed1295c3550092fd7a994ec49795a634ee33b117",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-09-17T13:34:58Z",
    "title_canon_sha256": "16ce703695188c5025452ac4b6d1dd70723f90c02f89cf600a62dd6140975cb2"
  },
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    "kind": "arxiv",
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