论文标题
通过状态约束参数，具有线性乘法梯度型噪声的多孔媒体系统的渐近介质问题
Asymptotic issue for porous media systems with linear multiplicative gradient-type noise via state constrained arguments
论文作者
论文摘要
本文的目的是提供必要和充分的条件，以维持随机耦合系统，并使用内部控件在一组规定的约束中，具有多孔介质组件和梯度型噪声。这项工作是[10]中结果的延续，因为我们考虑了发散类型噪声扰动的情况。另一方面，它提供了一个不同的框架，在该框架中，可以以最佳的速度获得准划分条件。与上述结果相比，在这里，我们通过重新制定方法将随机系统转化为随机确定性系统，然后我们研究随机集合的生存能力。作为应用，获得了随机多孔介质方程的稳定条件。
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This work is a continuation of the results in [10], as we consider the case of divergence type noise perturbation. On the other hand, it provides a different framework in which the quasi-tangency condition can be obtained with optimal speed. In comparison with the aforementioned result, here we transform the stochastic system into a random deterministic one, via the rescaling approach, then we study the viability of random sets. As an application, conditions for the stabilization of the stochastic porous media equations are obtained.
