Periodic solutions of a phase-field model with hysteresis

Periodic waves in unsaturated porous media with hysteresis

We consider a PDE system with degenerate hysteresis describing unsaturated flow in 3D porous media. Assuming that a time periodic forcing is prescribed on the boundary, we prove that a time periodic response exists as long as the amplitude of the forcing terms is small enough to keep the solution within the convexity domain of the hysteresis operator.

Symmetric periodic solutions of parabolic problems with hysteresis

We consider the heat equation in a multidimensional domain with nonlocal hysteresis feedback control in a boundary condition. Thermostat is our prototype model. We construct all periodic solutions with exactly two switching on the period and study their stability. Coexistence of several periodic solutions with different stability properties is proved to be possible. A mechanism of appearance and disappearance of periodic solutions is investigated.

带滞后的抛物型问题中相边界的性质

Properties of the phase boundary in the parabolic problem with hysteresis

研究含间断滞后算子的抛物型方程解的相边界性质，确定空间横向初始数据在特定空间下解的存在性及界面边界的Holder连续性或Lipschitz条件，证明非横向初始数据无带界面边界的解。

双周期粗糙表面上方向性接触角滞后区间的区域分解方法

A domain decomposition method for the directional contact angle hysteresis interval on doubly periodic rough surfaces

针对双周期粗糙表面润湿，提出两尺度交替区域分解方法计算方向性接触角滞后区间，揭示强各向异性并约束宏观润湿区域。

Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics

We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially…

Hysteresis and phase transitions in a lattice regularization of an ill-posed forward-backward diffusion equation

We consider a lattice regularization for an ill-posed diffusion equation with trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.