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math.AP2017
Chemotaxis model with subcritical exponent in nonlocal reaction
Shen Bian, Li Chen, Evangelos A. Latos
This paper deals with a parabolic-elliptic chemotaxis system with nonlocal type of source in the whole space. It's proved that the initial value problem possesses a unique global s…
math.AP2017
Blow-Up of Solutions to the Patlak-Keller-Segel Equation in Dimension
Li Chen, Heinz Siedentop
We prove a blow-up criterion for the solutions to the -dimensional Patlak-Keller-Segel equation in the whole space. The condition is new in dimension three and higher. In dimens…
math.AP2017
Wavefronts for a nonlinear nonlocal bistable reaction-diffusion equation in population dynamics
Li Chen, Evangelos Latos, Jing Li
The wavefronts of a nonlinear nonlocal bistable reaction-diffusion equation, \begin{align*} \frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}+u^2(1-J_σ*u)-du,\quad(t,x…