标题： 关于抛物-抛物型Keller-Segel方程的自相似稳定性 显示英文标题

标题： On the self-similar stability of the parabolic-parabolic Keller-Segel equation

摘要： 我们研究了平面中的抛物-抛物型Keller-Segel方程，并证明了在拟抛物-椭圆情形下，自相似解的非线性指数稳定性。 首先，我们进行摄动论证，以便通过利用抛物-椭圆Keller-Segel方程线性化算子的指数稳定性，得到与线性化算子第一分量的部分对应的半群的指数稳定性。 最后，我们采用纯半群分析来证明该系统在线性化以及适当的泛函空间中的非线性指数稳定性。 显示英文摘要

摘要： We consider the parabolic-parabolic Keller-Segel equation in the plane and prove the nonlinear exponential stability of the self-similar profile in a quasi parabolic-elliptic regime. We first perform a perturbation argument in order to obtain exponential stability for the semigroup associated to part of the first component of the linearized operator, by exploiting the exponential stability of the linearized operator for the parabolic-elliptic Keller-Segel equation. We finally employ a purely semigroup analysis to prove linear, and then nonlinear, exponential stability of the system in appropriated functional spaces.