应太阳集团tyc151cc王智诚教授和张亮教授的邀请，大连理工大学曹杨教授将于2025年12月11日-13日访问太阳集团tyc151cc，期间于12月12日举办专题学术报告。

报告题目：Threshold dynamics of traveling waves for monostable pseudo-parabolic equation

时 间：12月12日上午9:00.

地 点：腾讯会议715-857-502

报告摘要：In this talk, we focus on the global boundedness and asymptotic behavior of classical soThis report is about the traveling wave solutions to the pseudo-parabolic equation, a kind of non-classical diffusion equation characterized by the mixed third-order derivative term. We demonstrate that the ratio of the mixed third-order derivative coefficient to the diffusion coefficient $\frac{\tau}{D}$ can serve as a bifurcation parameter. In detail, when $\frac{\tau}{D}\leq 1$, the equation possesses monotone traveling waves; when $\frac{\tau}{D}>1$, traveling waves are not monotonic and oscillate around the steady state $u=1$. The precise form of the minimal wave speed $c^*(\tau,D)$ is also derived, exhibiting a monotonic increase with respect to $\tau$ and converging to $2\sqrt{D}$ as $\tau$ approaches $0$. Numerical simulations confirm and support our theoretical results. They further show that the larger the value of $\tau$ is, the more non-monotonic the traveling waves become. Our findings regarding oscillating traveling waves predict saturation overshoot---a behavior that contradicts classical diffusion-like behavior yet is widely observed in unsaturated porous media. Mathematically, the threshold value of $\frac{\tau}{D}$ reveals the essential role of the dynamic capillary effect in the fundamental overshoot mechanism.

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报告人简介

曹杨，大连理工大学教授、博士生导师。长期从事伪抛物方程的理论及应用的研究，成果发表于J. Funct. Anal.，J. Differential Equations，Nonlinearity，Discrete Contin. Dyn. Syst.等国际重要学术期刊。

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2025年12月10日