Optimal L2-decay of solutions to a nonlinear Schrödinger equation with sub-critical dissipative nonlinearity

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D-nonlinear Schrödinger equations with a sub-critical dissipative power nonlinearity. Our aim is to obtain two results. One asserts that, if a global solution decays more rapidly than t - d with d = 1...

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Veröffentlicht in:	Nonlinear differential equations and applications 2022, Vol.29 (4)
Hauptverfasser:	Kita, Naoyasu, Sato, Takuya
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Boundary value problems Mathematics Mathematics and Statistics Nonlinearity Optimization Schrodinger equation
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creator	Kita, Naoyasu Sato, Takuya
description	This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D-nonlinear Schrödinger equations with a sub-critical dissipative power nonlinearity. Our aim is to obtain two results. One asserts that, if a global solution decays more rapidly than t - d with d = 1 / ( p - 1 ) - 1 / 2 in L 2 , then it must be a trivial solution. The other one shows the existence of a solution decaying just at the rate of t - d in L 2 .
doi_str_mv	10.1007/s00030-022-00772-5
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title	Optimal L2-decay of solutions to a nonlinear Schrödinger equation with sub-critical dissipative nonlinearity
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