Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity - Kholyavka, O. T. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
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).