论文标题
非明显非自主夸张的永久性对于无限维微分方程
Permanence of nonuniform nonautonomous hyperbolicity for infinite-dimensional differential equations
论文作者
论文摘要
在本文中，我们研究了与Banach空间中的微分方程相关的进化过程的不均匀双波利度的稳定性。我们证明了线性进化过程的不均匀双曲线的稳健性，也就是说，我们表明，在扰动下，承认非均匀指数二分法的特性是稳定的。此外，我们提供条件以获得与非均匀指数二分法相关的投影的独特性和连续依赖性。我们还展示了在Banach空间中进化过程的一个例子，该过程接受了非均匀的指数二分法，并研究了扰动下非均匀双曲线的持久性。最后，我们证明了在扰动下非线性进化过程的非均匀双曲线溶液的持久性。
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution processes, that is, we show that the property of admitting a nonuniform exponential dichotomy is stable under perturbation. Moreover, we provide conditions to obtain uniqueness and continuous dependence of projections associated with nonuniform exponential dichotomies. We also present an example of evolution process in a Banach space that admits nonuniform exponential dichotomy and study the permanence of the nonuniform hyperbolicity under perturbation. Finally, we prove persistence of nonuniform hyperbolic solutions for nonlinear evolution processes under perturbations.
