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

  • O. T. Kholyavka

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).
Published
25.04.2014
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.
Section
Research articles