In this paper, we show the global well-posedness for periodic gKdV equations in the space H(T), s ≥ 1 2 for quartic case, and s > 5 9 for quintic case. These improve the previous results of Colliander et al in 2004. In particular, the result is sharp in the quartic case.

We prove global well-posedness for the defocusing cubic wave equation

Initial-boundary value problems for 1-dimensional ‘completely integrable’ equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the Dirichet data suffices to make the pr...

We report on new results concerning the global well-posedness, dissipativity and attractors of the damped quintic wave equations in bounded domains of R.

We prove global well-posedness for the radial defocusing cubic wave equation

the most costly operation in the oil exploration is the well network drilling. one of the most effectiveways to reduce the cost of drilling networks is decreasing the number of the required wells byselecting the optimum situation of the rig placement. in this paper, balas algorithm is used as a modelfor optimizing the cost function in oil well network, where the vertical and directional drillin...