摘要
该文研究一类由抛物方程和椭圆方程耦合的非线性Keller-Segel方程的局部零能控性.该方程不仅具有非线性的drift-diffuion项,而且具有非线性的人口增长项.作者利用抛物-椭圆结构的非局部特性将方程组化为单个非线性抛物型方程并利用Kakutani不动点定理证明了局部零能控性的存在性.
In this paper, we study the local controllability for a nonlinear Keller-Segel equation coupled by an elliptic partial differential equation and a parabolic one, in which nonlinearity lies both on its drift-diffusion term and population growth. We prove the local null controllability by Kakutani＇s fixed point theorem. The method is established on the nonlocal structure of the elliptic-parabolic equation so that it can be treated as a single nonlinear parabolic equation.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2017年第5期834-845,共12页
Acta Mathematica Scientia
基金
国家自然科学基金(61573012)
湖北省自然科学基金(2014CFB337)~~
