Averaged controllability for random evolution Partial Differential Equations

Lu Q, Zuazua E (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Journal De Mathematiques Pures Et Appliquees Elsevier

Book Volume: 105

Pages Range: 367-414

Journal Issue: 3

DOI: 10.1016/j.matpur.2015.11.004

Abstract

We analyze the averaged controllability properties of random evolution Partial Differential Equations. We mainly consider heat and Schrödinger 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 Schrödinger 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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Sichuan University (SCU) / 四川大学 CN China (CN) Universidad Autónoma de Madrid (UAM) ES Spain (ES)

How to cite

APA:

Lu, Q., & Zuazua, E. (2016). Averaged controllability for random evolution Partial Differential Equations. Journal De Mathematiques Pures Et Appliquees, 105(3), 367-414. https://dx.doi.org/10.1016/j.matpur.2015.11.004

MLA:

Lu, Qi, and Enrique Zuazua. "Averaged controllability for random evolution Partial Differential Equations." Journal De Mathematiques Pures Et Appliquees 105.3 (2016): 367-414.

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