6 papers
Optimal Spectral Lower Bounds and Nonradial Nonlinear Asymptotic Stability of a Family of Three-Dimensional Keller--Segel Self-Similar Blow-Up Solutions
Te Li, Yuwei Sun, Kaiqiang Zhang
This paper studies the spectral properties and nonlinear asymptotic stability of a family of finite-time self-similar blow-up solutions to the three-dimensional Keller--Segel syste…
Finite time blow-up for an inhomogeneous parabolic equation
Kaiqiang Zhang
We consider the inhomogeneous nonlinear heat equation \[ \partial_t u-Δu=|u|^{p-1}u+f(x),\qquad x\in\mathbb{R}^3,\quad p>5, \] where \(f\in L^\infty\cap C^{0,1}(\mathbb{R}^3)\). Fo…
On the existence and nonexistence of global solutions of the semilinear heat equation
Kaiqiang Zhang, Zhiyu Li
We consider the semilinear heat equation The well-known difficulty with this problem is that the potential well…
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…
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…
Set-theoretical solutions to the Hom-Yang-Baxter equation and Hom-cycle sets
Kaiqiang Zhang, Xiankun Du
Set-theoretic solutions to the Yang-Baxter equation have been studied extensively by means of related algebraic systems such as cycle sets and braces, dynamical versions of which h…