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Decay estimate and asymptotic behavior of small solutions to Schrödinger equations with subcritical dissipative nonlinearity. (English) Zbl 1435.35350
Kato, Keiichi (ed.) et al., Asymptotic analysis for nonlinear dispersive and wave equations. Proceedings of the international conference on asymptotic analysis for nonlinear dispersive and wave equations, Osaka University, Osaka, Japan, September 6–9, 2014. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 81, 121-138 (2019).
Summary: 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.
For the entire collection see [Zbl 1435.35006].

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
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