报告承办单位: 数学与统计学院

报告内容:  Wave-breaking criteria and persistence properties for the nonlocal Whitham-type equations

报告人姓名: 董晓芳

报告人所在单位: 太原理工大学

报告人职称/职务及学术头衔:讲师

报告时间: 2025年12月30日8:00-12:00

腾讯会议号：153-276-857，密码：135246

邀请人：刘斯丽

报告摘要:In this talk, we mainly focus some nonlocal Whitham-type equations which include the $b$-family equation, the generalized rod equation and hyperelastic rod equation, the generalized Fornberg-Whitham equation and two-component Fornberg-Whitham system. A class of priori estimates of $L^\infty$-norm of the solution $u$ to the corresponding equations is firstly constructed by making good use of the Osgood inequality. Then, based on this fact, some new wave-breaking criteria of the solutions for the equations which involve the $b$-family equation, the generalized rod equation, the hyperelastic rod equation and the generalized Fornberg-Whitham equation are obtained without the help of any conservation law properties. Finally, by the aid of the $L^1$-norm conservation of $\rho$ and the $L^2$-norm of $u$ with respect to a linear function of time $t$, we consider the local-in-space wave-breaking criterion of the solution for the two-component Fornberg-Whitham system by the characteristics line method. Moreover, the persistence properties of the solutions for the two-component Fornberg-Whitham system in weighted $L^p(\mathbb R)$ spaces are also investigated.

报告人简介: 董晓芳，太原理工大学数学学院讲师， 北京理工大学数学与统计学院博士。主要从事非线性色散水波方程定性性质的研究， 在期刊Commun、Nonlinear Sci.、Nonlinear Anal. Real World Appl.、Discrete Contin. Dyn. Syst. Ser. B、 J. Math. Phys.等发表论文12篇,，目前参与国家自然科学基金面上项目1项，主持山西省自然科学基金1项。