Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4622066 | Journal of Mathematical Analysis and Applications | 2008 | 12 Pages |
Abstract
This paper discusses a class of inhomogeneous nonlinear Schrödinger equation{i∂tu(t,x)=−Δu(t,x)−V(x)|u(t,x)|p−1u(t,x),u(0,x)=u0(x), where (t,x)∈R×R2(t,x)∈R×R2, V(x)V(x) satisfies some assumptions.By a constrained variational problem, we firstly define some cross-constrained invariant sets for the inhomogeneous nonlinear Schrödinger equation, then we obtain some sharp conditions for global existence and blow up of solutions. As a consequence it is shown that the solution is globally well-posed in Hr1(R2) with the H1H1-norm of the initial data u0u0 which is dominated by the minimal value of the constrained variational problem.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yanjin Wang,