Show simple item record

dc.contributor.authorCui, Jingen_US
dc.date.accessioned2017-04-25T08:00:12Z
dc.date.available2017-04-25T08:00:12Z
dc.date.issued2017-04-24en_US
dc.identifier.othervt_gsexam:10059en_US
dc.identifier.urihttp://hdl.handle.net/10919/77506
dc.description.abstractThe dissertation focuses on the nonlinear Schrodinger equation iu_t+u_{xx}+kappa|u|^2u =0, for the complex-valued function u=u(x,t) with domain t>=0, 0<=x<= L, where the parameter kappa is any non-zero real number. It is shown that the problem is locally and globally well-posed for appropriate initial data and the solution exponentially decays to zero as t goes to infinity under the boundary conditions u(0,t) = beta u(L,t) and beta u_x(0,t)-u_x(L,t) = ialpha u(0,t), where L>0, and alpha and beta are any real numbers satisfying alpha*beta<0 and beta does not equal 1 or -1. Moreover, the numerical study of controllability problem for the nonlinear Schrodinger equations is given. It is proved that the finite-difference scheme for the linear Schrodinger equation is uniformly boundary controllable and the boundary controls converge as the step sizes approach to zero. It is then shown that the discrete version of the nonlinear case is boundary null-controllable by applying the fixed point method. From the new results, some open questions are presented.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis item is protected by copyright and/or related rights. Some uses of this item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectNonlinear Schrodinger Equationen_US
dc.subjectContraction Mapping Principleen_US
dc.subjectBoundary Controlen_US
dc.titleBoundary Controllability and Stabilizability of Nonlinear Schrodinger Equation in a Finite Intervalen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairSun, Shu-Mingen_US
dc.contributor.committeememberLin, Taoen_US
dc.contributor.committeememberKim, Jong U.en_US
dc.contributor.committeememberYue, Pengtaoen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record