论文标题
一维凯勒 - 塞格方程的溶液的渐近收敛性
Asymptotic Convergence of Solutions for One-Dimensional Keller-Segel Equations
论文作者
论文摘要
本文的第二和第三作者是在[14]的一维凯勒 - 塞格方程的[14]有限维吸引子中构建的。他们还在[14，第7节]中指出，当灵敏度函数是线性函数时，方程将允许全局lyapunov函数。但是在那一刻，他们无法显示解决方案的渐近收敛性。然后，本文用于补充[14，第7节]的结果，通过证明作为$ t \至\ infty $，每个解决方案都必须通过使用lyapunov函数的lojasiewicz-simon梯度不平等来收敛到固定解决方案。
The second and third authors of this paper have constructed in [14] finite-dimensional attractors for the one-dimensional Keller-Segel equations. They have also remarked in [14, Section 7] that, when the sensitivity function is a linear function, the equations admit a global Lyapunov function. But at that moment they could not show the asymptotic convergence of solutions. This paper is then devoted to supplementing the results of [14, Section 7] by showing that, as $t \to \infty$, every solution necessarily converges to a stationary solution by using the Łojasiewicz-Simon gradient inequality of the Lyapunov function.
