Title:Scattering Theory of Linear and Nonlinear Waves: A Unified New Paradigm

Speaker：Avy Soffer (The distinguished Professor)  

                 Rutgers University

报告时间(第一讲):7月15日周一8:00-9:00（北京时间）

Zoom link:  

https://rutgers.zoom.us/j/93162693013?pwd=sfHtFIMQ4ee3Lh2R5CaIxoFm9fC2Ln.1

摘要：

I will present a new approach to Mathematical Scattering of multichannel Dispersive and Hyperbolic Equations.

In this approach we identify the large time behavior of such equations, both linear and non-linear, for general (large) data and interactions terms which can be space-time dependent. In particular, for the NLS equations with spherically symmetric data and Interaction terms, we prove that all global solutions in H^1 converge to a smooth and localized function plus a free wave, in 5 or more dimensions. Similar result holds for 3,4 dimensions, though the argument proving localization is different.

We also show similar results in any dimension for localized type of interactions, provided they decay fast enough. We show breakdown of the standard Asymptotic Completeness conjecture if the interaction is time dependent and decays like r^{-2} at infinity.

Many of these results extend to the non-radial case, for NLS, NLKG and Bi-harmonic NLS in three or more dimensions. Furthermore, we prove Local-Decay Estimates for Time dependent potentials in 5 or more dimensions. Finally, we apply this approach to N-body scattering, and prove AC for three quasi-particle scattering.

This is based on joint works with Baoping Liu and Xiaoxu Wu.

报告人简介：

  Avy Soffer，美国罗格斯大学数学系（Rutgers University）杰出教授，美国数学会会士，主要从事数学物理与偏微方程的研究，其研究成果在Ann. Math., JAMS, Invent. Math. Duke J. Math.等国际著名期刊发表论文100余篇。学术上2006年在西班牙国际数学家大会上（ICM）作45分钟特邀报告，也曾担任GAFA杂志的编委，现为Letter in Math. Phy.杂志编委。