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L∞C(ℝn)-decay of classical solutions for nonlinear Schrödinger equations*

Published online by Cambridge University Press:  14 November 2011

Nakao Hayashi  and
Masayoshi Tsutsumi
Nakao Hayashi
Affiliation:
Department of Applied Physics, Waseda University, Tokyo 160, Japan
Masayoshi Tsutsumi
Affiliation:
Department of Applied Physics, Waseda University, Tokyo 160, Japan
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Synopsis

We study the initial value problem for the nonlinear Schrödinger equation

Under suitable regularity assumptions on f and ø and growth and sign conditions on f, it is shown that the maximum norms of solutions to (*) decay as t→² ∞ at the same rate as that of solutions to the free Schrödinger equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 104 , Issue 3-4 , 1986 , pp. 309 - 327
Copyright
Copyright © Royal Society of Edinburgh 1986

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