Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity
AbstractIn 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).
How to Cite
KholyavkaO. T. “Hyperbolic Variational Inequality of the Third Order With Variable Exponent of Nonlinearity”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 4, Apr. 2014, pp. 518–530, http://umj.imath.kiev.ua/index.php/umj/article/view/2154.