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Shun Takizawa

Publications and source records attributed to Shun Takizawa.

6 recordsLinked to original sources
arXiv2026

Asymptotic behavior for the damped Schrödinger equation with nonlinear dissipation

We consider large time asymptotics of solutions to the damped Schrödinger 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.

math.AP↗
arXiv2026

Sharp asymptotic behavior of solutions to damped nonlinear Schrödinger equations

We consider large time asymptotics for damped nonlinear Schrödinger equations. It is known that the nonlinear solution asymptotically behaves like a linear solution when time $t$ tends to infinity in the energy space. We prove that its convergence rate can be refined and the obtained rate is sharp if initial data belong to certain function spaces. This result partially solves open problems concerning the optimal decay rate of scattering.

math.AP↗
arXiv2025

Strichartz estimates in Wiener amalgam spaces for Schrödinger equations with at most quadratic potentials

For Schrödinger equations with potentials which grow at most quadratically at spatial infinity, we prove Strichartz estimates in Wiener amalgam spaces. These estimates provide a stronger recovery of local-in-space regularity than the classical Strichartz estimates in Lebesgue spaces. Our result is a generalization of the results on Strichartz estimates in Wiener amalgam spaces by Cordero and Nicola, which are stated for the potentials $V(x) = 0,|x|^2/2, -|x|^2/2$.

math.AP↗
arXiv2024

Short time asymptotics of the fundamental solutions for Schrödinger equations with non-smooth potentials

This paper deals with Schrödinger equations with potentials which are time-dependent non-smooth and at most quadratic growth. In the case where potentials are smooth with respect to spatial variables, fundamental solutions have explicit formulas in short time by D. Fujiwara. On the otherhand in the case where ones are non-smooth, we cannot expect that fundamental solutions have similar formula as above because dispersive estimates fail to hold in general. We show that a principal part of an asymptotic form of the fundamental solution has similar form as above even in the case where a potential is in $C^2$ with respect to spatial variables.

math.AP↗