3 papers
math.AP2026
Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems
Xinru Cao, Mario Fuest
We consider the Neumann initial boundary value problem associated to the chemotaxis system \begin{align}\label{prob:abstract}\tag{} \begin{cases} u_t = \big((u+1)^{m-1} u_x…
math.AP2025
Finite-time blow-up in fully parabolic quasilinear Keller-Segel systems with supercritical exponents
Xinru Cao, Mario Fuest
We examine the possibility of finite-time blow-up of solutions to the fully parabolic quasilinear Keller--Segel model \begin{align}\tag{}\label{prob:star} \begin{cases} u_t…
math.AP2024
Superlinear transmission in an indirect signal production chemotaxis system
Xinru Cao
In this paper, the indirect signal production system with nonlinear transmission is considered \[ \left\{ \begin{array}{lll} & u_t = Îu-\nabla\cdot(u \nabla v), \\ \displaystyle &…