Lu Q, Zuazua E (2016)
Publication Type: Journal article
Publication year: 2016
Book Volume: 105
Pages Range: 367-414
Journal Issue: 3
DOI: 10.1016/j.matpur.2015.11.004
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.
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://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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