Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

O.M. Buhrii; O.T. Kholyavka; P.Ya. Pukach; M.I. Vovk

doi:10.15330/cmp.12.2.419-433

Authors

O.M. Buhrii Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine https://orcid.org/0000-0002-1698-5559
O.T. Kholyavka Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine https://orcid.org/0000-0002-5843-7374
P.Ya. Pukach Lviv Polytechnic National University, 5 Mytropolyt Andrei str., 79013, Lviv, Ukraine https://orcid.org/0000-0002-0359-5025
M.I. Vovk Lviv Polytechnic National University, 5 Mytropolyt Andrei str., 79013, Lviv, Ukraine https://orcid.org/0000-0002-7818-7755

https://doi.org/10.15330/cmp.12.2.419-433

Keywords:

nonlinear hyperbolic equation, Cauchy problem, variable exponent of nonlinearity, Lebesgue space with variable exponent

Published online: 2020-12-27

Abstract

We investigate weak solutions of the Cauchy problem for the third order hyperbolic equations with variable exponent of the nonlinearity. The problem is considered in some classes of functions namely in Lebesgue spaces with variable exponents. The sufficient conditions of the existence and uniqueness of the weak solutions to given problem are found.

Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

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