On connection between the order of a stationary one-dimensional dispersive equation and the growth of its convective term

A boundary value problem for a stationary nonlinear dispersive equation of 2l+1 order with a convective term in the form u^ku_x, k\in N was considered on an interval (0,L). The existence, uniqueness and continuous dependence of a regular solution as well as a relation between the order l and critical values of k of the equation have been established.

Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation

In this paper, we investigate the problem for optimal control of a viscous generalized \theta -type dispersive equation (VG \theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG \theta -type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.