Averaged controllability for random evolution Partial Differential Equations

作者：Lu, Qi; Zuazua, Enrique^*

来源：Journal de Mathematiques Pures et Appliquees, 2016, 105(3): 367-414.

DOI：10.1016/j.matpur.2015.11.004

• Random evolution Partial
• Differential Equations
• Averaged controllability
• Averaged observability
• Schrodinger equation
• Heat equation

We analyze the averaged controllability properties of random evolution Partial Differential Equations. We mainly consider heat and Schrodinger equations with random parameters, although the problem is also formulated in an abstract frame. We show that the averages of parabolic equations lead to parabolic-like dynamics that enjoy the null-controllability properties of solutions of heat equations in an arbitrarily short time and from arbitrary measurable sets of positive measure. In the case of Schrodinger equations we show that, depending on the probability density governing the random parameter, the average may behave either as a conservative or a parabolic-like evolution, leading to controllability properties, in average, of very different kind.

• 出版日期2016
• 单位四川大学