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arXiv · 2609.07322

Asymptotic behavior for the damped Schr\"{o}dinger equation with nonlinear dissipation

Takahisa Inui·Shun Takizawa
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Abstract

We consider large time asymptotics of solutions to the damped Schr\"{o}dinger equation with the nonlinear dissipation in the mass-subcritical case. We prove that the optimal $L^2$-decay rate of the nonlinear solution coincides with that of the corresponding linear solution even in the presence of nonlinear dissipation. Moreover, we give the optimal convergence rate for scattering for any power in the mass-subcritical regime.

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Takahisa Inui, Shun Takizawa. 2026-09-07. Asymptotic behavior for the damped Schr\"{o}dinger equation with nonlinear dissipation. https://arxiv.org/abs/2609.07322

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