Аннотация:
Решается задача восстановления матричного потенциала V(x), x>0, по заданному оператору реакции R:u(0,t)↦ux(0,t), t>0.
Выявлены связи этой задачи с теорией граничного управления, что позволило получить аналоги классических уравнений Гельфанда–Левитана–Крейна. Установлена базисность семейства векторных экспонент, связанного со спектральными характеристиками краевой задачи. Доказана управляемость соответствующей системы при граничном управлении
u(0,t)=f(t).
Образец цитирования:
С. А. Авдонин, М. И. Белишев, С. А. Иванов, “Граничное управление и матричная обратная задача для уравнения utt−uxx+V(x)u=0”, Матем. сб., 182:3 (1991), 307–331; S. A. Avdonin, M. I. Belishev, S. A. Ivanov, “Boundary control and a matrix inverse problem for the equation utt−uxx+V(x)u=0”, Math. USSR-Sb., 72:2 (1992), 287–310
\RBibitem{AvdBelIva91}
\by С.~А.~Авдонин, М.~И.~Белишев, С.~А.~Иванов
\paper Граничное управление и~матричная обратная задача для уравнения $u_{tt}-u_{xx}+V(x)u=0$
\jour Матем. сб.
\yr 1991
\vol 182
\issue 3
\pages 307--331
\mathnet{http://mi.mathnet.ru/sm1296}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1110068}
\zmath{https://zbmath.org/?q=an:0782.93054|0735.93042}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..72..287A}
\transl
\by S.~A.~Avdonin, M.~I.~Belishev, S.~A.~Ivanov
\paper Boundary control and a~matrix inverse problem for the equation $u_{tt}-u_{xx}+V(x)u=0$
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 2
\pages 287--310
\crossref{https://doi.org/10.1070/SM1992v072n02ABEH002141}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992JT05200001}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sm1296
https://www.mathnet.ru/rus/sm/v182/i3/p307
Эта публикация цитируется в следующих 37 статьяx:
Pavel Kurasov, Operator Theory: Advances and Applications, 293, Spectral Geometry of Graphs, 2024, 463
Shanshan Hu, Yongxin Yuan, “The Anti-symmetric Solution of the Matrix Equation AXA⊤=B on a Null Subspace”, Results Math, 79:3 (2024)
Yinlan Chen, Yawen Lan, “The best approximation problems between the least-squares solution manifolds of two matrix equations”, MATH, 9:8 (2024), 20939
Nitesh Kumar, Tanmay Sarkar, Manmohan Vashisth, “Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide”, CAC, 2024
S. Avdonin, J. Edward, Y. Zhao, “Shape, velocity, and exact controllability for the wave equation on a graph with cycle”, Алгебра и анализ, 35:1 (2023), 3–32; St. Petersburg Math. J., 35:1 (2024), 1–23
A. V. Borovskikh, “Traveling Wave Method”, Diff Equat, 59:5 (2023), 629
Shanshan Hu, Yongxin Yuan, “The symmetric solution of the matrix equation AXB=D on subspace”, Comp. Appl. Math., 41:8 (2022)
Sergei Avdonin, Julian Edward, “An inverse problem for quantum trees with observations at interior vertices”, NHM, 16:2 (2021), 317
S A Avdonin, A S Mikhaylov, V S Mikhaylov, J C Park, “Inverse problem for the Schrödinger equation with non-self-adjoint matrix potential”, Inverse Problems, 37:3 (2021), 035002
Bao-Zhu Guo, Sergei A. Ivanov, “Finite dimensional control of multichannel systems”, Journal of Differential Equations, 296 (2021), 213
Avdonin S.A., Ivanov S.A., Wang J.-M., “Inverse Problems For the Heat Equation With Memory”, Inverse Probl. Imaging, 13:1 (2019), 31–38
Sergei Avdonin, Nina Avdonina, Yuanyuan Zhao, “Exact Controllability for the Wave Equation on Star Graphs”, IFAC-PapersOnLine, 52:2 (2019), 30
Sergei Avdonin, “Control, Observation and Identification Problems for the Wave Equation on Metric Graphs”, IFAC-PapersOnLine, 52:2 (2019), 52
Ammar Khanfer, Alexander Bukhgeim, “Inverse problem for one-dimensional wave equation with matrix potential”, Journal of Inverse and Ill-posed Problems, 27:2 (2019), 217
Sergei A. Ivanov, Jun Min Wang, “Controllability of a multichannel system”, Journal of Differential Equations, 264:4 (2018), 2538
Sergei Avdonin, Julian Edward, “Exact Controllability for String with Attached Masses”, SIAM J. Control Optim., 56:2 (2018), 945
L. Pandolfi, “Dynamical identification of a space varying coefficient in a system with persistent memory”, Journal of Mathematical Analysis and Applications, 465:1 (2018), 140
A. L. Sakhnovich, R. Ibragimov, V. Vougalter, M.W. Wong, “Evolution of Weyl Functions and Initial-Boundary Value Problems”, Math. Model. Nat. Phenom., 11:2 (2016), 111
Sergei Avdonin, Serge Nicaise, “Source identification problems for the wave equation on graphs”, Inverse Problems, 31:9 (2015), 095007
A. L. Sakhnovich, “Dynamical and spectral Dirac systems: response function and inverse problems”, Journal of Mathematical Physics, 56:11 (2015), 112702
Цитирование в формате AMSBIB
Обратная связь: