The Forced Non-Linear Schroedinger Equation with a Potential on the Half-Line
Weder, Ricardo
arXiv, 0304351 / Harvested from arXiv
Text on arXiv
In this paper we prove that the initial-boundary value problem for the forced non-linear Schroedinger equation with a potential on the half-line is locally and (under stronger conditions) globally well posed, i.e. that there is a unique solution that depends continuously on the force at the boundary and on the initial data. We allow for a large class of unbounded potentials. Actually, for local solutions we have no restriction on the grow at infinity of the positive part of the potential, and for global solutions very mild assumptions that allow, for example, for exponential grow.
Publié le : 2003-04-23
Classification:  Mathematics - Analysis of PDEs,  Mathematical Physics,  35Q40, 35Q55, 35R30 
@article{0304351,
     author = {Weder, Ricardo},
     title = {The Forced Non-Linear Schroedinger Equation with a Potential on the
  Half-Line},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0304351}
}

Weder, Ricardo. The Forced Non-Linear Schroedinger Equation with a Potential on the
  Half-Line. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0304351/