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One-Sided Boundary Control for the Process of Oscillations Described by the Equation k(x)[k(x)u x (x,t)] x − u tt (x,t) = 0

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Abstract

This article concerns the boundary control on the side x = 0 when the other side x = l is fixed. The corresponding process of oscillations is studied for the time interval T > 0 and is described by the generalized solution of the equation

$$k\left( x \right)\left[ {k\left( x \right)u_x \left( {x,t} \right)} \right]_x u_{tt} \left( {x,t} \right) = 0$$

This solution belongs to the class that admits the existence of finite energy for any time moment t.

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REFERENCES

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Authors
  1. V. A. Ilyin
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Ilyin, V.A. One-Sided Boundary Control for the Process of Oscillations Described by the Equation k(x)[k(x)u x (x,t)] x − u tt (x,t) = 0. Journal of Mathematical Sciences 114, 1461–1472 (2003). https://doi.org/10.1023/A:1022205029149

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  • DOI: https://doi.org/10.1023/A:1022205029149

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