L∞C(ℝn)-decay of classical solutions for nonlinear Schrödinger equations
- 1 January 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 104 (3-4) , 309-327
- https://doi.org/10.1017/s0308210500019235
Abstract
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.Keywords
This publication has 23 references indexed in Scilit:
- On solutions of the initial value problem for the nonlinear Schr dinger equations in one space dimensionMathematische Zeitschrift, 1986
- Classical solutions of nonlinear Schrödinger equationsmanuscripta mathematica, 1986
- The asymptotic behavior of nonlinear Schrödinger equationsBulletin of the American Mathematical Society, 1984
- Global existence of small solutions to nonlinear evolution equationsJournal of Differential Equations, 1982
- Decay and asymptotics for higher dimensional nonlinear wave equationsJournal of Differential Equations, 1982
- Time decay for nonlinear wave equations in two space dimensionsmanuscripta mathematica, 1982
- Classical solutions of nonlinear Schrödinger equations in higher dimensionsMathematische Zeitschrift, 1981
- Global classical solutions of nonlinear wave equationsMathematische Zeitschrift, 1981
- Time dependent nonlinear Schrödinger equationsmanuscripta mathematica, 1979
- Equations de Schrödinger non linéaires en dimension deuxProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1979