Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501603 | Journal of Differential Equations | 2005 | 35 Pages |
Abstract
We study the Schrödinger equation iâtu+Îu+V0u+V1u=0 on R3Ã(0,T), where V0(x,t)=|x-a(t)|-1, with aâW2,1(0,T;R3), is a coulombian potential, singular at finite distance, and V1 is an electric potential, possibly unbounded. The initial condition u0âH2(R3) is such that â«R3(1+|x|2)2|u0(x)|2dx<â. The potential V1 is also real valued and may depend on space and time variables. We prove that if V1 is regular enough and at most quadratic at infinity, this problem is well-posed and the regularity of the initial data is conserved for the solution. We also give an application to the bilinear optimal control of the solution through the electric potential.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Lucie Baudouin, Otared Kavian, Jean-Pierre Puel,