二维二次非线性schrÖdinger方程的非齐次dirichlet边值问题

Pub Date : 2020-01-01 DOI:10.2206/kyushujm.74.375

N. Hayashi, E. Kaikina

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引用次数: 0

摘要

研究二次非线性Schrödinger方程的非齐次dirichlet边值问题，认为这是解的大时渐近性的一个临界情况。利用自由Schrödinger群的经典能量法和因子分解技术，给出了方程小解渐近性的初始数据和边界数据的充分条件。

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INHOMOGENEOUS DIRICHLET-BOUNDARY VALUE PROBLEM FOR TWO-DIMENSIONAL QUADRATIC NONLINEAR SCHRÖDINGER EQUATIONS

We consider the inhomogeneous Dirichlet–boundary value problem for the quadratic nonlinear Schrödinger equations, which is considered as a critical case for the largetime asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schrödinger group.

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