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33 papers · 1 filter
Local well-posedness of a nonlinear Fokker-Planck model
Yekaterina Epshteyn, Chang Liu, Chun Liu +1
Noise or fluctuations play an important role in the modeling and understanding of the behavior of various complex systems in nature. Fokker-Planck equations are powerful mathematic…
On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit
Jiangyan Liang, Ning Jiang, Chun Liu +2
Most of the previous studies on the well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion syst…
Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces
Wei Yan, Yimin Zhang, Yongsheng Li +1
We consider the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili (RMKP) equation \begin{align*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\partial_{x}(u^{2})\right…
On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
Patrik Knopf, Chun Liu
In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace--Beltrami equation o…
Pointwise convergence problem of Ostrovsky equation with rough data and random data
Wei Yan, Qiaoqiao Zhang, Jinqiao Duan +1
In this paper, we consider the pointwise convergence problem of free Ostrovsky equation with rough data and random data. Firstly, we show the almost everywhere pointwise convergenc…
Effective Wave Factorization for a Stochastic Schrödinger Equation
Ao Zhang, Jinqiao Duan
We study the homogenization of a stochastic Schrödinger equation with a large periodic potential in solid state physics. Denoting by the period, the potential is scal…