Nonlocal hyperbolic Stokes system with variable exponent of nonlinearity

O. M. Buhrii; O. T. Kholyavka; T. M. Bokalo

doi:10.30970/ms.60.2.173-179

O. M. Buhrii Ivan Franko National University of Lviv https://orcid.org/0000-0002-1698-5559
O. T. Kholyavka Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NASU
T. M. Bokalo Ivan Franko National University of Lviv

DOI: https://doi.org/10.30970/ms.60.2.173-179

Keywords: hyperbolic Stokes system;, weak solution;, variable exponent of nonlinearity;, nonlocal term.

Abstract

In this paper, we study the problem for a nonlinear hyperbolic Stokes system of the second order with an integral term.
Sufficient conditions for the uniqueness of the weak solution of this problem are found in a bounded domain. The nonlinear term of the system contains a variable exponent of nonlinearity, which is a function of spatial variables.
The problem is studied in ordinary Sobolev spaces and generalized Lebesgue spaces, which is quite natural in this case.

Author Biographies

O. M. Buhrii, Ivan Franko National University of Lviv

Ivan Franko National University of Lviv

O. T. Kholyavka, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NASU

Pidstryhach Institute for Applied Problems
of Mechanics and Mathematics of NASU

T. M. Bokalo, Ivan Franko National University of Lviv

Ivan Franko National University of Lviv

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