WELL-POSEDNESS FOR DEGENERATE SCHRODINGER EQUATIONS

被引：17

作者：

Cicognani, Massimo ^{[1
]}

Reissig, Michael ^{[2
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, I-40126 Bologna, Italy

[2] Tech Univ Bergakad Freiberg, Fak Math & Informat, Inst Angew Anal, D-09596 Freiberg, Germany

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2014年 / 3卷 / 01期

关键词：

Schrodinger equations; time-depending Hamiltonian; Cauchy problem; Levi conditions; Gevrey well-posedness; CAUCHY-PROBLEM;

D O I：

10.3934/eect.2014.3.15

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial value problem for Schrodinger type equations 1/i partial derivative(t)u - a(t) Delta(x) u + Sigma(n)(j=1) b(j) (t,x) partial derivative(xj) u = 0 with a(t) vanishing of finite order at t = 0 proving the well-posedness in Sobolev and Gevrey spaces according to the behavior of the real parts nb(j) (t, x) as t -> 0 and vertical bar x vertical bar -> infinity. Moreover, we discuss the application of our approach to the case of a general degeneracy.

引用

页码：15 / 33

页数：19

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