On a parabolic sine-gordon model

Cheng，Xinyu1; Li，Dong3; Quan，Chaoyu2,3; Yang，Wen4,5

2021-11-01

10.4208/NMTMA.OA-2021-0040

Numerical Mathematics-Theory Methods and Applications   Impact Factor & Quartile

1004-8979

2079-7338

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.

Backward differentiation formula Implicit-explicit scheme Sine-Gordon equation

SCI

English

Others

Basic and Applied Basic Research Foundation of Guangdong Province[2020A1515010336];

WOS:000695218700010

2-s2.0-85115777547

Scopus

1.Department of Mathematics,University of British Columbia,Vancouver,V6T 1Z2,Canada
2.SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China
3.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
4.Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan,P.O. Box 71010,430071,China
5.Innovation Academy for Precision Measurement Science and Technology,Chinese Academy of Sciences,Wuhan,430071,China

Cheng，Xinyu,Li，Dong,Quan，Chaoyu,et al. On a parabolic sine-gordon model[J]. Numerical Mathematics-Theory Methods and Applications,2021,14(4):1068-1084.

Cheng，Xinyu,Li，Dong,Quan，Chaoyu,&Yang，Wen.(2021).On a parabolic sine-gordon model.Numerical Mathematics-Theory Methods and Applications,14(4),1068-1084.

Cheng，Xinyu,et al."On a parabolic sine-gordon model".Numerical Mathematics-Theory Methods and Applications 14.4(2021):1068-1084.