题目: Global dynamics around 2-solitons for the nonlinear damped Klein-Gordon equation

报告人：Kenji Nakanishi (京都大学)

时间: 3月18日周五上午10:00-11:00

Zoom ID 736 190 7370

密码：122595

摘要：This is joint work with Kenjiro Ishizuka (Kyoto). We study global behavior of solutions to the Klein-Gordon equation with a damping and a focusing power nonlinearity on the Euclidean space. In the one-dimensional case, Cote, Martel and Yuan (ARMA 2021) proved the soliton resolution conjecture completely in the energy space: any solution with finite energy either blows up in finite time or asymptotic to a superposition of solitons that are logarithmically getting away from each other. A natural question is then to describe the correspondence between the initial data and the different types of solutions. In general dimensions, Cote, Martel, Yuan and Zhao (CMP 2021) proved that 2-solitons form a manifold of initial data with codimension 2 in the energy space. We concentrate on a neighborhood of the 2-solitons and give a complete classification of solutions into 5 different types with manifold structure. An important step in the proof is to show that the direction of instability is not essentially affected by the soliton interaction even if it changes the growth rate of instability.I will also discuss about the case of 3-solitons, where we have to face the new difficulty of soliton merger.