Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 34 min ago
PreprintCC BY-NC-ND 4.0HAL

The sharp and non-sharp threshold phenomenon in buffered and Go-or-Grow systems

  • Ruben Taieb
  • Arnaud Ducrot
Open at sourcePDFCite

Abstract

We investigate the threshold phenomenon for a broad class of partially degenerate, coupled systems of reaction-diffusion-ODE equations with a buffered or dormant compartment. When initialized with a class of compactly supported function, we prove the existence of a sharp threshold separating extinction and propagation for a general class of switching functions. We derive an expression for the derivative of the threshold with respect to some parameters, and give results on the optimal switching rate minimizing this threshold. Finally, we contrast these dynamics with a bistable "Go-or-Grow" model, and show that the non-invertibility of the ground solution map may yield a non-sharp transition zone characterized by a continuous family of discontinuous ground states.

Related

  1. Sharp bounds and asymptotic profiles for Lane-Emden systems at the Serrin threshold
    Shiguang Ma, Shengyang Zang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Blow-up or grow-up for the focusing 3D cubic NLS with a repulsive inverse-power potential at the mass--energy threshold
    Alex H. Ardila, Zuyu Ma, Ying Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. A threshold phenomenon for embeddings of Euclidean snowflakes and impossibility of dimension reduction
    Assaf Naor, Kevin Ren
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. The Sharp Ellipticity Threshold for W1,1-Regularity
    Franz Gmeineder
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and L2-Critical Terms
    Yongpeng Chen, Zhipeng Yang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{taieb2026sharp,
  title = {{The sharp and non-sharp threshold phenomenon in buffered and Go-or-Grow systems}},
  author = {Ruben Taieb and Arnaud Ducrot},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05760746v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The sharp and non-sharp threshold phenomenon in buffered and Go-or-Grow systems
AU  - Ruben Taieb
AU  - Arnaud Ducrot
PY  - 2026
DA  - 2026/09/20
PB  - HAL
UR  - https://hal.science/hal-05760746v1
AB  - We investigate the threshold phenomenon for a broad class of partially degenerate, coupled systems of reaction-diffusion-ODE equations with a buffered or dormant compartment. When initialized with a class of compactly supported function, we prove the existence of a sharp threshold separating extinction and propagation for a general class of switching functions. We derive an expression for the derivative of the threshold with respect to some parameters, and give results on the optimal switching rate minimizing this threshold. Finally, we contrast these dynamics with a bistable "Go-or-Grow" model, and show that the non-invertibility of the ground solution map may yield a non-sharp transition zone characterized by a continuous family of discontinuous ground states.
ER  -