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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 \[ u_t = Δu - \frac{1}{u^2} \quad \text{in } \mathcal{B} \times (0,T), \quad u|_{\partial \mathcal{B}} = 1, \] where $…
math.AP2025
Axisymmetric type II blowup solutions to the three-dimensional Keller-Segel system
Thomas Y. Hou, Van Tien Nguyen, Peicong Song
We construct axisymmetric solutions to the three-dimensional parabolic-elliptic Keller-Segel system that blow up in finite time. In particular, the singularity is of type II, which…
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…