Pith Number

pith:K4MSCOTL

pith:2026:K4MSCOTL5QZYBYBCUALJTV6XDY

not attested not anchored not stored refs resolved

Local and global solutions to continuous fragmentation-coagulation equations with vanishing diffusion and unbounded fragmentation and coagulation rates

Sergey Shindin

Fragmentation-coagulation equations with vanishing diffusion are locally well-posed when fragmentation dominates, and globally solvable for power rates in every dimension.

arxiv:2605.14452 v1 · 2026-05-14 · 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{K4MSCOTL5QZYBYBCUALJTV6XDY}

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

In the special case of power rates, we demonstrate existence of global in time classical solutions in all spatial dimensions d≥1 and without any restrictions on the size of input data.

C2weakest assumption

The diffusion and coagulation processes are suitably dominated by the fragmentation process, allowing the estimates to close for local well-posedness.

C3one line summary

Local well-posedness and global existence of classical solutions are established for fragmentation-coagulation PDEs with vanishing diffusion under fragmentation domination.

References

48 extracted · 48 resolved · 0 Pith anchors

[1] A. S. Ackleh and B. G. Fitzpatrick. Modeling aggregation and growth processes in an algal population model: Analysis and computations.J. Math. Biol., 35:480– 502, 1997 1997

[2] R.A. Adams and J.F. Fournier.Sobolev Spaces. Academic Press, 2003 2003

[3] M. Aizenman and T.A. Bak. Convergence to equilibrium in a system of reacting polymers.Comm. Math. Phys., 65(3):203–230, 1979 1979

[4] H. Amann. Operator-Valued Fourier Multipiers, Vector-Valued Besov Spaces, and Applications.Math. Nachr., 186:5–56, 1997 1997

[5] H. Amann. Coagulation-fragmentation processes.Arch. Rat. Mech. Anal., 151:339–366, 2000 2000

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:06.882001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5719213a6bec3380e022a01699d7d71e3b6483a933f17b3cd1a11b621bb8c0fb

Aliases

arxiv: 2605.14452 · arxiv_version: 2605.14452v1 · doi: 10.48550/arxiv.2605.14452 · pith_short_12: K4MSCOTL5QZY · pith_short_16: K4MSCOTL5QZYBYBC · pith_short_8: K4MSCOTL

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/K4MSCOTL5QZYBYBCUALJTV6XDY \
  | 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: 5719213a6bec3380e022a01699d7d71e3b6483a933f17b3cd1a11b621bb8c0fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e79ea5f88801a176507627b15ef3e0f97a8fa02bae5acd3bca47ab0ac66e9c0a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-14T06:45:35Z",
    "title_canon_sha256": "e3a62bbcb98163706740a9d5ce0f3be6a7ebb972a142884cf37d63b385164993"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14452",
    "kind": "arxiv",
    "version": 1
  }
}