Initial-Boundary Value Problems for Generalized Dispersive Equations of Higher Orders Posed on Bounded Intervals

Abstract

Initial-boundary value problems for nonlinear dispersive equations of evolution of order $$2l+1, \;l\in \mathbb {N}$$ with a convective term of the form $$u^ku_x,\;k\in \mathbb {N}$$ have been considered on intervals $$(0,L),\;L\in (0,+\infty )$$ . Definitions of regular and critical values of k as functions of l have been given. The existence and uniqueness of global regular solutions as well as exponential decay of them for small initial data have been established.