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

• Datum: 2014
• Hauptverfasser: Kholyavka, O. T., Холявка, О. Т.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2014
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/2154
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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...