Abstract
In this paper, we deal with the boundary value problems without initial condition for Schrodinger systems in cylinders. We establish several results on the existence and uniqueness of solutions.
Highlights
The initial boundary value for the Schrödinger equation in cylinders with base containing conical points was established in [ ]. Such a problem for parabolic systems was studied in Sobolev spaces with weights [ ]
Following the method in [ ], we prove the existence of solutions uh of problems with initial conditions t = h
In Section, we present the results on the unique solvability of problems with initial condition for Schrödinger systems in cylinders
Summary
The initial boundary value for the Schrödinger equation in cylinders with base containing conical points was established in [ ]. Such a problem for parabolic systems was studied in Sobolev spaces with weights [ ]. The boundary value problem without initial condition for parabolic equation was investigated in [ ]. We consider the boundary value problem without initial condition for Schrödinger systems in cylinders. By letting h → –∞, the solvability of a problem without initial condition is obtained. In Section , we present the results on the unique solvability of problems with initial condition for Schrödinger systems in cylinders.
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