Advanced Studies in Pure Mathematics

Decay estimate and asymptotic behavior of small solutions to Schrödinger equations with subcritical dissipative nonlinearity

Naoyasu Kita and Yoshihisa Nakamura

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Abstract

This manuscript presents some results on the decay estimate and asymptotic behavior of small solutions to the Cauchy problem of 1D Schrödinger equations with a sub-critical dissipative nonlinearity. Our aim is to determine the explicit lower bound of the nonlinear power for which certain a priori estimate of the solution works well.

Article information

Source
Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, K. Kato, T. Ogawa and T. Ozawa, eds. (Tokyo: Mathematical Society of Japan, 2019), 121-138

Dates
Received: 1 April 2016
Revised: 16 July 2016
First available in Project Euclid: 31 October 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1572545243

Digital Object Identifier
doi:10.2969/aspm/08110121

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B40: Asymptotic behavior of solutions

Keywords
nonlinear Schrödinger equation decay estimate asymptotic behavior dissipative nonlinearity sub-critical nonlinearity

Citation

Kita, Naoyasu; Nakamura, Yoshihisa. Decay estimate and asymptotic behavior of small solutions to Schrödinger equations with subcritical dissipative nonlinearity. Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, 121--138, Mathematical Society of Japan, Tokyo, Japan, 2019. doi:10.2969/aspm/08110121. https://projecteuclid.org/euclid.aspm/1572545243


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