Pith Number

pith:FPSEAPNJ

pith:2026:FPSEAPNJYVLWGXRUKOJL6G2GEB

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Bilinear control to trajectories of 1D degenerate parabolic equations in moving domains

Alfredo S. Gamboa, Andr\'e da Rocha Lopes, Luis P. Yapu

Bilinear control on the reaction coefficient achieves exact controllability to any nearby positive trajectory for a one-dimensional semilinear degenerate parabolic equation in a time-evolving domain.

arxiv:2605.15499 v1 · 2026-05-15 · math.AP

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Claims

C1strongest claim

We deal with the exact controllability to a positive trajectory of a one-dimensional semilinear degenerate equation governed via the coefficient of the reaction term in bounded domains that evolve in time.

C2weakest assumption

The specific estimates derived for the linearized degenerate operator in the moving domain are sufficient to satisfy the conditions of the local inversion theorem without further restrictions on the trajectory or degeneracy strength.

C3one line summary

Exact controllability to positive trajectories is established for 1D semilinear degenerate parabolic equations in moving domains via bilinear reaction-term control using a local inversion method with tailored estimates.

References

33 extracted · 33 resolved · 0 Pith anchors

[1] F . Alabau-Boussouira, P . Cannarsa, and P . Cannarsa. Exact controllability to eigensolutions for evolution equations of parabolic type via bilinear control.Nonlinear Differential Equations and Appli 2022

[2] F . Alabau-Boussouira, P . Cannarsa, and G. Fragnelli. Carleman estimates for degenerate parabolic operators with applications to null controllability . Journal of Evolution Equations, 6:161 – 204, 20 2006

[3] F . Alabau-Boussouira, P . Cannarsa, and G. Leugering. Control and stabilization of degenerate wave equations.SIAM Journal on Control and Optimization, 55(3):2052–2087, 2017 2052

[4] F . Alabau-Boussouira, P . Cannarsa, and C. Urbani. Bilinear control of evolution equations with unbounded lower order terms. Application to the Fokker–Planck equation.Comptes Rendus. Mathématique, 36 2024

[5] V . Alekseev, V . Tikhomorov, and S. Formin.Optimal control. Contemporary Soviet Mathematics, 1987 1987

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:01.835875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2be4403da9c557635e345392bf1b462067d3dc784fc3866a1dd2f8187a56fdf1

Aliases

arxiv: 2605.15499 · arxiv_version: 2605.15499v1 · doi: 10.48550/arxiv.2605.15499 · pith_short_12: FPSEAPNJYVLW · pith_short_16: FPSEAPNJYVLWGXRU · pith_short_8: FPSEAPNJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FPSEAPNJYVLWGXRUKOJL6G2GEB \
  | 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: 2be4403da9c557635e345392bf1b462067d3dc784fc3866a1dd2f8187a56fdf1

Canonical record JSON

{
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    "abstract_canon_sha256": "994eb99d996102aa8e4afce406c09e87d560cabf4ac466f2ca78a92efe35642a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-15T00:32:45Z",
    "title_canon_sha256": "1c362c9b8eddde2c96d643c18bd4ef001b90bab479d8445e93f50f172f0d8adf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15499",
    "kind": "arxiv",
    "version": 1
  }
}