43 citations · 201 across the 69 of their papers we have counts for
9 papers · 1 filter
An F-modulated stability framework for multistep methods
Dong Li, Chaoyu Quan, Wen Yang
We introduce a new -modulated energy stability framework for general linear multistep methods. We showcase the theory for the two dimensional molecular beam epitaxy mode…
From KP-I lump solution to travelling waves of Gross-Pitaevskii equation
Yong Liu, Zhengping Wang, Juncheng Wei +1
Let be an nondegenerate lump solution to KP-I (Kadomtsev-Petviashvili-I) equation $$\partial_x^4q-2\sqrt{2}\partial_x^2q-3\sqrt{2}\partial_x((\partial_xq) ^2)-2\partial_y^…
On a sinc-type MBE model
Xinyu Cheng, Dong Li, Chaoyu Quan +1
We introduce a new sinc-type molecular beam epitaxy model which is derived from a cosine-type energy functional. The landscape of the new functional is remarkably similar to the cl…
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…
The BDF3/EP3 scheme for MBE with no slope selection is stable
Dong Li, Chaoyu Quan, Wen Yang
We consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. We employ a third order backward differentiation (BDF3) in…
Generic properties of free boundary problems in plasma physics
Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar +1
We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain var…
Multi-Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain
Daniel Gomez, Juncheng Wei, Wen Yang
In this paper we consider the existence and stability of multi-spike solutions to the fractional Gierer-Meinhardt model with periodic boundary conditions. In particular we rigorous…