Subcritical Kuramoto–Sivashinsky-type equation on a half-line

In this paper we are interested in the global existence and large-time behavior of solutions to the initial-boundary value problem for subcritical Kuramoto–Sivashinsky-type equation where the nonlinear term depends on the unknown function u and its derivative ux and satisfy the estimate with σ 0,ρ 1 such that The aim of this paper is to prove the global existence of solutions to the initial-boundary value problem (0.1) in subcritical case, when the nonlinear term has a time decay rate less than that of the linear terms of Eq. (0.1). Also we find the main term of the asymptotic representation of solutions.