asymptotic analysis 1axisymmetric solutions 1keller-segel model 1mass concentration 1type ii blowup 1
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math.AP2026
Axisymmetric type II blowup solutions to the three-dimensional Keller-Segel system
Thomas Y. Hou, Van Tien Nguyen, Peicong Song
The paper constructs axisymmetric solutions of the three‑dimensional parabolic‑elliptic Keller‑Segel system that develop finite‑time type II blowup, with mass concentrating along a…
math.AP2025
Nonradial Quenching Profile for a MEMS Model
Hsuan-Lin Liao, Van Tien Nguyen
We construct a quenching solution to the parabolic MEMS model \[ u_t = Îu - \frac{1}{u^2} \quad \text{in } \mathcal{B} \times (0,T), \quad u|_{\partial \mathcal{B}} = 1, \] where…
math.AP2024
On the stability of blowup solutions to the complex Ginzburg-Landau equation in R^d
Jiajie Chen, Thomas Y. Hou, Van Tien Nguyen +1
Building upon the idea in \cite{HNWarXiv24}, we establish stability of the type-I blowup with log correction for the complex Ginzburg-Landau equation. In the amplitude-phase repres…