中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：袁旭（香港中文大学）
题 目：The cubic Klein-Gordon equation with damping （II）
时 间：2024.05.20（星期一）15:00-17:00
地 点：思源楼S813
摘 要: In this mini-course, we will study the long-time asymptotic behavior of 1D focusing cubic Klein-Gordon equation with damping. We start with the Local and Global Cauchy Theory and then we will introduce the background of the ground state for this equation. Next, we will recall a remarkable result due to Eduard Feireisl. More precisely, we will recall that in large time, any global solution converges strongly, at least for a subsequence, to the zero function or to a sum of decoupled solitary waves. Last, we describe a more detailed convergence result, for the whole sequence of time, with a characterization of all the possible asymptotic configurations and a precise convergence rate. Prerequisites for this course are the bases of Real Analysis, of Functional Analysis, and of Graduate level PDE Theory. This course is based on the Lecture Notes of Yvan Martel for the 2024 Master 2 course at Université Paris-Saclay.
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