PreprintCC BY 4.0arXiv
Blow-Up and Life-Span for Nonlinear Hardy-Hénon Parabolic Equations
Abstract
We consider the nonlinear Hardy-Hénon parabolic equation $ u_t=Δu+|x|^l|u|^αu,$ t>0, x∈ℝN or x∈ℝN∖{0}, with N≥1, l>−min{2,N}, α>0, with nonnegative initial datum u0. We first establish new criteria for finite-time blow-up. We then derive optimal upper bounds for the life-span Tmax(λφ) of solutions arising from the initial datum u0=λφ. These estimates establish a precise dependence of Tmax(λφ) on both the initial profile φ and the parameter λ in the small and large-amplitude regimes.
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BibTeX
@misc{slimene2026blowup,
title = {{Blow-Up and Life-Span for Nonlinear Hardy-Hénon Parabolic Equations}},
author = {Byrame Ben Slimene and Slim Tayachi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08662},
eprint = {2611.08662},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08662},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Blow-Up and Life-Span for Nonlinear Hardy-Hénon Parabolic Equations
AU - Byrame Ben Slimene
AU - Slim Tayachi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08662
UR - https://arxiv.org/abs/2611.08662
AB - We consider the nonlinear Hardy-Hénon parabolic equation $ u_t=Δu+|x|^l|u|^αu,$ t>0, x∈ℝ^N or x∈ℝ^N∖{0}, with N≥1, l>−min{2,N}, α>0, with nonnegative initial datum u_0. We first establish new criteria for finite-time blow-up. We then derive optimal upper bounds for the life-span T_max(λφ) of solutions arising from the initial datum u_0=λφ. These estimates establish a precise dependence of T_max(λφ) on both the initial profile φ and the parameter λ in the small and large-amplitude regimes.
ER -