کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609665 1338523 2016 41 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Null-controllability of the Kolmogorov equation in the whole phase space
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Null-controllability of the Kolmogorov equation in the whole phase space
چکیده انگلیسی

We prove the null controllability, in arbitrary positive time, of the Kolmogorov equation ∂t+v⋅∇x−△v∂t+v⋅∇x−△v with (x,v)∈Rd×Rd(x,v)∈Rd×Rd, with a control region of the form ω=ωx×ωvω=ωx×ωv, where both ωxωx and ωvωv are open subsets of RdRd that are sufficiently spread out throughout the whole space RdRd. The proof is based on, on the one hand, a spectral inequality in RdRd with an observation on ωxωx, and, on the other hand, a Carleman-based observability inequality for a family of parabolic operators, ∂t−iv⋅ξ−△v∂t−iv⋅ξ−△v, coupled with a knowledge of the decay rate of the free solutions of the Kolmogorov equation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 260, Issue 4, 15 February 2016, Pages 3193–3233
نویسندگان
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