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Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity

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Ukrainian Mathematical Journal Aims and scope

In Sobolev spaces with variable exponent, we consider the problem for a semilinear hyperbolic variational inequality of the third order. We establish conditions for the existence of a solution u of this problem such that u ∈ L ∞((0, T); V 1,0(Ω)), u t  ∈ L ∞((0, T); V 1,0(Ω)) ∩ L p(x)(Q T ), and u tt  ∈ L ∞((0, T); L 2(Ω)), where V 1,0(Ω) ⊂ H 1(Ω).

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Authors and Affiliations

  1. Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    O. T. Kholyavka

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  1. O. T. Kholyavka
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 4, pp. 518–530, April, 2014.

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Kholyavka, O.T. Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity. Ukr Math J 66, 580–593 (2014). https://doi.org/10.1007/s11253-014-0955-2

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  • DOI: https://doi.org/10.1007/s11253-014-0955-2

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