blow-up 1finite-codimension stability 1inhomogeneous PDE 1nonlinear heat equation 1self-similar solutions 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.AP2026
Finite time blow-up for an inhomogeneous parabolic equation
Kaiqiang Zhang
The paper analyzes a nonlinear heat equation with a bounded spatial source term and proves that for many non‑radial initial data there exist finite‑time blow‑up solutions whose res…
math.AP2025
Infinitely many self-similar blow-up profiles for the Keller-Segel system in dimensions 3 to 9
Van Tien Nguyen, Zhi-An Wang, Kaiqiang Zhang
Based on the method of matched asymptotic expansions and Banach fixed point theorem, we rigorously construct infinitely many self-similar blow-up profiles for the parabolic-ellipti…
math.AP2024
On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher
Charles Collot, Kaiqiang Zhang
We consider the parabolic-elliptic Keller-Segel system in spatial dimensions , which corresponds to the mass supercritical case. Some solutions become singular in finite ti…