特邀杭州师范大学数学学院余星辰老师作学术报告

发布单位:数学与统计学院(公共数学教学部)创建者:尚林发布时间:2024-01-10浏览量:10

报告题目:Bifurcation and dynamics of periodic solutions to the Rayleigh-Plesset equation

报告人:余星辰

报告时间:2024121日上10:00-11:00

报告地点:藕舫楼702

主持人:邹瑞


报告摘要:In this paper, we study the oscillation of a gas-filled spherical bubble immersed in an infinite domain of incompressible liquid under the influence of a time-periodic acoustic field. The oscillation is described by the Rayleigh-Plesset equation, which is derived from the Navier-Stokes equation under the assumptions of spherical symmetry. Taking the initial radius $R_0$, or the initial instantaneous partial pressure $P_{g0}$, of the gas-filled bubble as a parameter, we present a saddle-node bifurcation of periodic solutions to the Rayleigh-Plesset equation in the parameter space, provided the mean value of of applied pressure is greater than the vapor pressure. Further, we show that the Rayleigh-Plesset equation has two classes of periodic solutions, as $R_0$ (resp. $P_{g0}$) tends to $+\infty$, the first class of solutions uniformly diverges to $+\infty$ at the rate of $R_0^5$ (resp. $P_{g0}^{5/2}$), while the second class converges to $0$ at the rate of $R_0^{-5}$ (resp. $P_{g0}^{-5/2}$). As for the case where the density of the liquid $\rho$ is chosen as a parameter, we observe an interesting nonlinear phenomenon that, for some $\rho$, the Rayleigh-Plesset equation may possess four positive $T$-periodic solutions: two of them are stable, while the rest of them are unstable. This is quite different from the phenomenon that occurs when $R_0$ (or $P_{g0}$) is chosen as a parameter.


报告人简介:余星辰,2022年博士毕业于南京信息工程大学,攻读博士学位期间受国家留学基金委资助,在捷克科学院数学研究所联合培养,现为杭州师范大学数学学院讲师。主要研究方向是奇性微分方程周期解的分支和动力学行为,相关研究成果发表在J. Differential Equations, Physica D, Proc. R. Soc. Edinb. Sect. A Math.等国际期刊上。

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