65 citations · 188 across the 26 of their papers we have counts for
5 papers · 1 filter
Energy-dissipation for time-fractional phase-field equations
Dong Li, Chaoyu Quan, Jiao Xu
We consider a class of time-fractional phase field models including the Allen-Cahn and Cahn-Hilliard equations. We establish several weighted positivity results for functionals dri…
Sharp convergence to steady states of Allen-Cahn
Dong Li, Chaoyu Quan, Tao Tang +1
In our recent work we found a surprising breakdown of symmetry conservation: using standard numerical discretization with very high precision the computed numerical solutions corre…
On symmetry breaking of Allen-Cahn
Dong Li, Chaoyu Quan, Tao Tang +1
We consider numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numer…
On a parabolic sine-Gordon model
Xinyu Cheng, Dong Li, Chaoyu Quan +1
We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the o…
How to Define Dissipation-Preserving Energy for Time-Fractional Phase-Field Equations
Chaoyu Quan, Tao Tang, Jiang Yang
There exists a well defined energy for classical phase-field equations under which the dissipation law is satisfied, i.e., the energy is non-increasing with respect to time. Howeve…