Yujuan Chen | Searcharxiv

arXiv2021

Self-propulsion dynamics of small droplets on general surfaces with curvature gradient

We study theoretically the self-propulsion dynamics of a small droplet on general curved surfaces by a variational approach. A new reduced model is derived based on careful computations for the capillary energy and the viscous dissipation in the system. The model describes quantitatively the spontaneous motion of a liquid droplet on general surfaces. In particular, it recovers previous models for droplet motion on the outside surface of a cone. In this case, we derive a scaling law of the displacement $s\sim t^{1/3}$ of a droplet with respect to time $t$ by asymptotic analysis. Theoretical results are in good agreement with experiments in previous literature without adjusting the friction coefficient in the model.

physics.flu-dyn↗

arXiv2014

Initial and boundary blow-up problem for $p$-Laplacian parabolic equation with general absorption

In this article, we investigate the initial and boundary blow-up problem for the $p$-Laplacian parabolic equation $u_t-Δ_p u=-b(x,t)f(u)$ over a smooth bounded domain $Ω$ of $\mathbb{R}^N$ with $N\ge2$, where $Δ_pu={\rm div}(|\nabla u|^{p-2}\nabla u)$ with $p>1$, and $f(u)$ is a function of regular variation at infinity. We study the existence and uniqueness of positive solutions, and their asymptotic behaviors near the parabolic boundary.

math.AP↗