@Article{NMTMA-14-1068,
author = {Cheng , XinyuLi , DongQuan , Chaoyu and Yang , Wen},
title = {On a Parabolic Sine-Gordon Model},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {4},
pages = {1068--1084},
abstract = {<p style="text-align: justify;">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 one-dimensional case we classify all bounded steady
states and exhibit some explicit solutions. For the numerical discretization we employ first order IMEX, and second order BDF2 discretization without any additional
stabilization term. We rigorously prove the energy stability of the numerical schemes
under nearly sharp and quite mild time step constraints. We demonstrate the striking
similarity of the parabolic sine-Gordon model with the standard Allen-Cahn equations with double well potentials.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2021-0040},
url = {http://global-sci.org/intro/article_detail/nmtma/19530.html}
}