Pith Number

pith:SFU3RHFE

pith:2026:SFU3RHFELSWWJ2IVKC56FXIE45

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Refined estimates of the propagation speed in porous medium equation of combustion type

Fan Wu, Suying Liu

For a family of combustion nonlinearities the asymptotic spreading speed in the porous medium equation receives an explicit characterization of the o(1) correction.

arxiv:2605.13361 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

for a family of functions of combustion type, we refine the estimates of the asymptotic speed of the transition solution and provide a precise characterization of the lower order term o(1). Our result also reveals that there is no unified characterization of the lower order term for general combustion type functions f.

C2weakest assumption

The initial data is a multiple of a fixed compactly supported function and f belongs to a specific family of combustion-type nonlinearities that permits the refined expansion; the precise conditions on this family are not stated in the abstract.

C3one line summary

For a family of combustion-type nonlinearities, the transition solution spreads at speed 2 y0 sqrt(t) with a precisely characterized lower-order term that depends on the specific form of f and is not universal across all such f.

References

15 extracted · 15 resolved · 0 Pith anchors

[1] S. Angenent. The zero set of a solution of a parabolic equation.J. Reine Angew. Math, 390(1988), 79–96. 23 1988

[2] D. Aronson, M. G. Crandall, and L. A. Peletier. Stabilization of solutions of a degenerate nonlinear diffusion problem.Nonlinear Analysis: Theory, Methods and Applications,6 (1982), 1001–1022 1982

[3] D. G. Aronson. Density-dependent interaction–diffusion systems. InDynamics and modelling of reactive systems, (1980), 161–176, Elsevier, 1980

[4] A. de Pablo. and J. L. V´ azquez. Travelling waves and finite propagation in a reaction- diffusion equation.Journal of differential equations,93(1991), 19–61 1991

[5] Y. Du and B. Lou. Spreading and vanishing in nonlinear diffusion problems with free boundaries.Journal of the European Mathematical Society,17(2015), 2673–2724 2015

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:48.133120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9169b89ca45cad64e91550bbe2dd04e74e8c17b9670459e44bb8b759939620e9

Aliases

arxiv: 2605.13361 · arxiv_version: 2605.13361v1 · doi: 10.48550/arxiv.2605.13361 · pith_short_12: SFU3RHFELSWW · pith_short_16: SFU3RHFELSWWJ2IV · pith_short_8: SFU3RHFE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SFU3RHFELSWWJ2IVKC56FXIE45 \
  | 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: 9169b89ca45cad64e91550bbe2dd04e74e8c17b9670459e44bb8b759939620e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6265de277527f63dbd017d2e34c7772d0d8a434183e2271a89ef75fbc60669e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T11:21:58Z",
    "title_canon_sha256": "fa6079e3c15176134358bf21373a8cd2a565230eaa285bcbe9885a57ef53e5c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13361",
    "kind": "arxiv",
    "version": 1
  }
}