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

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.

Nonlocal hyperbolic Stokes system with variable exponent of nonlinearity

“…Some local energy decay estimate of solutions for such problem is obtained. Hyperbolic equations of third order with variable exponent of nonlinearity is considered in [14].…”