4 citations · 22 across the 16 of their papers we have counts for
23 papers · 1 filter
Infinite time bubble towers in the fractional heat equation with critical exponent
Li Cai, Jun Wang, Jun-Cheng Wei +1
In this paper, we consider the fractional heat equation with critical exponent in for \begin{equation*} u_t=-(-Δ)^su+|u|^{\frac{4s}{n-2s}}u,\quad (…
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^…
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…
Partial regularity of stable solutions to the fractional Gel'fand-Liouville equation
Ali Hyder, Wen Yang
We analyze stable weak solutions to the fractional Gel'fand problem \begin{equation*} (-Δ)^su=e^u\quad\mathrm{in}\quad Ω\subset\mathbb{R}^n. \end{equation*} We prove that the dimen…