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Владимир Ильин, V. Il'in, Евгений Моисеев, E. Moiseev (2005)
Оптимизация граничных управлений колебаниями струны@@@Optimization of boundary controls of string vibrations, 60
(2000)
Boundary Control of the Vibration Process at Two Ends in Terms of a Generalized Solution of the Wave Equation with Finite Energy
V. Il'in, E. Moiseev (2005)
Optimization of boundary controls of string vibrationsRussian Mathematical Surveys, 60
(2000)
Boundary Control of the Vibration Process at Two Ends in Terms of a Generalized Solution of the Wave Equation with Finite Energy, Differ
(1960)
On the Solvability of Mixed Problems for a Hyperbolic and a Parabolic Equation, Uspekhi Mat
V. Il'in (1960)
THE SOLVABILITY OF MIXED PROBLEMS FOR HYPERBOLIC AND PARABOLIC EQUATIONSRussian Mathematical Surveys, 15
(2006)
Minimization of the Integral of the Absolute Value of the Derivative of the Boundary Control by the Displacement Raised to an Arbitrary Degree p ≥ 1 for an Arbitrary Sufficiently Large Time Interval
V.A. Il’in (1960)
On the Solvability of Mixed Problems for a Hyperbolic and a Parabolic EquationUspekhi Mat. Nauk, 15
We consider a boundary value problem for the wave equation with given initial conditions and with boundary conditions of the second kind at one end of the string and boundary conditions of the first kind at the other end of the string. We assume the boundary conditions to ensure that the solution of the problem (in the class of generalized functions) satisfying the initial conditions at the initial time t = 0 satisfies given terminal conditions at the terminal time t = T. We clarify the relationship between the functions µ(t) and ν(t) in the boundary conditions and the given functions specifying the initial and terminal states. We obtain closed-form analytic expressions for the functions µ(t) and ν(t) minimizing the boundary energy functional.
Differential Equations – Springer Journals
Published: Jul 19, 2009
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