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Robust Stability of the Attractor of a Nonlinear Wave Equation Without Uniqueness of the Solution

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We study the qualitative behavior of a nonlinear wave equation with nonsmooth interaction function subjected to the action of external bounded disturbances. It is proved that the global attractor of the multivalued semiflow generated by the solutions of unperturbed problem is stable in a sense of input-to-state with respect to disturbances.

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Authors and Affiliations

  1. T. Shevchenko Kyiv National University, Akad. Glushkov Ave., 4E, Kyiv, 03022, Ukraine

    O. Kapustyan & T. Yusypiv

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  1. O. Kapustyan
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  2. T. Yusypiv
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Correspondence to T. Yusypiv.

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Translated from Neliniini Kolyvannya, Vol. 25, No. 2-3, pp. 198–206, April–September, 2022.

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Kapustyan, O., Yusypiv, T. Robust Stability of the Attractor of a Nonlinear Wave Equation Without Uniqueness of the Solution. J Math Sci 274, 850–860 (2023). https://doi.org/10.1007/s10958-023-06648-y

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