標(biāo)題：Dynamics of equations in electrodynamics through perturbative techniques
報(bào)告時(shí)間：2025年2月21日（星期五）10：00-11：00
報(bào)告地點(diǎn)：人民大街校區(qū)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院二樓會(huì)議室
主講人：楊佳琦
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容簡(jiǎn)介：
Differential equations modeling the motion of N charged particles are subject to small but complex delays and advances, defined implicitly by the solutions of the system. To understand the dynamics of such systems, we introduce functional perturbations—incorporating delays or advances—into ordinary differential equations. We demonstrate that near certain special solutions of the unperturbed equations, there exist solutions of the perturbed functional equations. Moreover, we establish smooth dependence of these solutions on parameters. We develop methods to quantify the size of allowable perturbations using a computer-assisted approach. Finally, we present some recent advances in the study of a point charge interacting with a small plasma, including results on existence and uniqueness of solutions to the Vlasov-Poisson system and their asymptotic behavior.
主講人簡(jiǎn)介：
楊佳琦，同濟(jì)大學(xué)，特聘研究員。于2021年在美國(guó)佐治亞理工學(xué)院獲博士學(xué)位，2021-2022 年在美國(guó)布朗大學(xué)從事博士后研究，2022-2023 年在美國(guó)克拉克森大學(xué)任助理教授，現(xiàn)為同濟(jì)大學(xué)特聘研究員。長(zhǎng)期從事動(dòng)力系統(tǒng)動(dòng)力學(xué)行為的研究，與美國(guó)佐治亞理工學(xué)院、布朗大學(xué)、加拿大麥吉爾大學(xué)等動(dòng)力系統(tǒng)、微分方程領(lǐng)域的權(quán)威學(xué)者保持著密切的學(xué)術(shù)合作，受邀在美國(guó)布朗大學(xué)、德州農(nóng)工大學(xué)、加拿大多倫多大學(xué)等國(guó)外高校以及北美多地舉辦的會(huì)議上作報(bào)告10余次。
