Critical Ostrovskiy-type equation on a half-line

Abstract

We consider the initial-boundary-value problem for the Ostrovskiy type equation on a half-line. We study traditionally important problems of a theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary-value problem and the asymptotic behavior of solutions for large time in the critical case, when the time decay of the nonlinearity has the same rate as that of the linear part of the equation.