Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 53 min ago
PreprintarXiv licencearXiv

Sharp Quantitative Convergence of Compactly Supported Aggregation-Diffusion

  • Yunhong Deng
Open at sourcePDFDOICite

Abstract

We establish the quantitative convergence of nonlinear aggregation-diffusion equations in dimension one, with sublinear attraction kernel and degenerate diffusion higher than quadratic. In these models, steady state is known to be the unique, compactly supported, and radial decreasing probability distribution. In this paper, we work with compactly supported densities in dimension one, we prove these solutions converge to the steady state exponentially fast.

Related

  1. Quantitative Stability Of Aggregation-Diffusion Under Local Attraction
    Yunhong Deng
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  2. Compactly Supported Solutions near a Nehari Critical Value
    J. I. Dıaz, J. Hernandez, Y. Ilyasov
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Compactly supported instability of Riemannian Schwarzschild–Tangherlini metrics
    Erwann Delay
    HALPreprintCC BY 4.0Full textGeometry & topologyMathematical physicsHALarXiv
  4. A new approach to compactly supported stationary Euler flows
    Alberto Enciso, Antonio J. Fernández
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. A note on existence of smooth solution to Jacobian equation for compactly supported smooth data in ℝ2
    Animesh Jana
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{deng2026sharp,
  title = {{Sharp Quantitative Convergence of Compactly Supported Aggregation-Diffusion}},
  author = {Yunhong Deng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29000},
  eprint = {2610.29000},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29000},
}
RIS
TY  - UNPB
TI  - Sharp Quantitative Convergence of Compactly Supported Aggregation-Diffusion
AU  - Yunhong Deng
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29000
UR  - https://arxiv.org/abs/2610.29000
AB  - We establish the quantitative convergence of nonlinear aggregation-diffusion equations in dimension one, with sublinear attraction kernel and degenerate diffusion higher than quadratic. In these models, steady state is known to be the unique, compactly supported, and radial decreasing probability distribution. In this paper, we work with compactly supported densities in dimension one, we prove these solutions converge to the steady state exponentially fast.
ER  -