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The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables. (English. Russian original) Zbl 1129.93021
Autom. Remote Control 68, No. 2, 337-350 (2007); translation from Avtom. Telemekh. 68, No. 2, 138-151 (2007).
Summary: A new representation is proved of the solutions of initial boundary value problems for the equation of the form \(u_{xx}(x, t) + r(x)u _{x}(x, t) - q(x)u(x, t) = u _{tt}(x, t) + \mu (x)u _{t}(x, t)\) in the section (under boundary conditions of the 1st, 2nd, or 3rd type in any combination). This representation has the form of the Riemann integral dependent on the x and t over the given section.
MSC:
93C20 Control/observation systems governed by partial differential equations
35B37 PDE in connection with control problems (MSC2000)
35L20 Initial-boundary value problems for second-order hyperbolic equations
93C05 Linear systems in control theory
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