Nonlinear Schroedinger Equation with Inhomogeneous Dirichlet Boundary Data

Journal Article · Mon Aug 01 04:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1914730· OSTI ID:20699351

Bu, Charles; Tsutaya, Kimitoshi; Chenying, Zhang ^[1]

---

1. Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02481 (United States)

In this article we study the following nonlinear Schroedinger equation iu{sub t}={delta}u-g vertical bar u vertical bar {sup p-1}u in a domain {omega} subset of R{sup n} with initial condition u(x,0)={phi}(x) and the Dirichlet boundary condition u(x,t)=Q(x,t) on {partial_derivative}{omega}, where {phi}, Q are given smooth functions. The nonlinear term contributes a negative term to the energy (i.e., g<0). We present the existence theorem for a global solution of finite energy when p{<=}1+2/n.

• OSTI ID: 20699351
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIRICHLET PROBLEM
FUNCTIONAL ANALYSIS
FUNCTIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
RIEMANN SPACE
SCHROEDINGER EQUATION