Pith Number

pith:6WMSIHIX

pith:2026:6WMSIHIXZC2VMEBCPCKC6CQZAJ

not attested not anchored not stored refs resolved

Boundary null-controllability for the beam equation with classical structural damping

Julian Edward, Sergei Avdonin

The damped beam equation reaches null state from the boundary for every damping strength up to 2 and for almost every strength above 2.

arxiv:2605.14371 v1 · 2026-05-14 · math.OC · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6WMSIHIXZC2VMEBCPCKC6CQZAJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove null controllability for all ρ ≤ 2. For ρ >2, we show null controllability for arbitrary T>0 holds for almost all ρ, but fails for a dense subset of (2,∞).

C2weakest assumption

The well-posedness of the damped beam equation under the specified boundary conditions and the validity of the controllability criteria (such as observability inequalities) for the given ranges of ρ.

C3one line summary

Null controllability holds for the beam equation with structural damping ρ for all ρ ≤ 2 and almost all ρ > 2.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] G. Avalos and I. Lasiecka, ”Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation”. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 3, 601–616 2003

[2] F. Ammar-Khodja, A. Benabdallah, M. Gonz´ alez-Burgos, L. de Teresa, Minimal time for the null controllability of parabolic systems: The effect of the condensation index ofcomplex sequences”, J. Funct 2014

[3] Null-controllability for the beam equation with struc- tural damping 2025

[4] Null-controllability for the beam equation with frac- tional structural damping

[5] In preparation

Receipt and verification

First computed	2026-05-17T23:39:07.824395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f599241d17c8b556102278942f0a1902440f1c92262d5a4fb6f800e59bd2cac9

Aliases

arxiv: 2605.14371 · arxiv_version: 2605.14371v1 · doi: 10.48550/arxiv.2605.14371 · pith_short_12: 6WMSIHIXZC2V · pith_short_16: 6WMSIHIXZC2VMEBC · pith_short_8: 6WMSIHIX

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6WMSIHIXZC2VMEBCPCKC6CQZAJ \
  | 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: f599241d17c8b556102278942f0a1902440f1c92262d5a4fb6f800e59bd2cac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fd20e50d48b971cd698055b6d780c4eece4e4a4bc6afd242ecc9333e9b85de3",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-14T04:49:29Z",
    "title_canon_sha256": "63adf7ec10713f80148bf4043671ec80701f07b82e43cd994322a2339be30969"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14371",
    "kind": "arxiv",
    "version": 1
  }
}