Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity
Abstract
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).
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 4, pp 580-593.
Citation Example: Kholyavka O. T. Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity // Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 518–530.
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