A General Scattering theory for Nonlinear and Non-autonomous Schroedinger Type Equations- A Brief description

no code implementations • 28 Dec 2020 • Baoping Liu, Avy Soffer

We give a short description of the proof of asymptotic-completeness for NLS-type equations, including time dependent potential terms, with radial data in three dimensions.

Analysis of PDEs Mathematical Physics Mathematical Physics 35P25, 35Q55, 47A40

Remark On The Notion Of Adapted Conformal And Other Estimates

no code implementations • 28 Dec 2020 • Avy Soffer

I describe a way to modify the multipliers of a-priori estimates, so as to include potential perturbations of the Laplacian.

Analysis of PDEs 35P15

L^p Boundedness of the Scattering Wave Operators of Schroedinger Dynamics with Time-dependent Potentials and applications

no code implementations • 28 Dec 2020 • Avy Soffer, Xiaoxu Wu

This paper establishes the $L^p$ boundedness of wave operators for linear Schr\"odinger equations in $\mathbb{R}^3$ with time-dependent potentials.

Analysis of PDEs 35P25, 35Q55, 47A40

Global existences and asymptotic behavior for semilinear heat equation

no code implementations • 28 Dec 2020 • Avy Soffer, Yifei Wu, Xiaohua Yao

In this paper, we consider the global Cauchy problem for the $L^2$-critical semilinear heat equations $ \partial_t h=\Delta h\pm |h|^{\frac4d}h, $ with $h(0, x)=h_0$, where $h$ is an unknown real function defined on $ \R^+\times\R^d$.

Analysis of PDEs 35K05, 35B40, 35B65