Asymptotic behavior of solutions to a dissipative nonlinear Schrödinger equation with time dependent harmonic potentials

2022/05/29 by Kawamoto, Masaki, Sato, Takuya · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.14605

Abstract

We consider the Cauchy problem of a dissipative nonlinear Schrödinger equation with a time dependent harmonic potential. We find a critical situation that the L²-norm of dissipative solutions decays or not and which is decided by a nonlinear power and time decay order of harmonic potential.

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