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Solution of mixed problems with boundary elastic-force control for the telegraph equation

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Abstract

In terms of a finite-energy generalized solution of the telegraph equation, for any time interval T, we consider the problem on the boundary elastic-force control u x (0, t) = µ(t) at the endpoint x = 0 for the process described by the Klein-Gordon-Fock equation under the condition that the other endpoint x = l is either fixed, or free, or is controlled by an elastic force. For any time interval T, we obtain the solution u(x, t) in closed form.

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References

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    I. N. Smirnov

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  1. I. N. Smirnov
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Original Russian Text © I.N. Smirnov, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 3, pp. 433–441.

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Smirnov, I.N. Solution of mixed problems with boundary elastic-force control for the telegraph equation. Diff Equat 47, 429–437 (2011). https://doi.org/10.1134/S0012266111030141

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  • DOI: https://doi.org/10.1134/S0012266111030141

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