36 citations · 69 across the 28 of their papers we have counts for
4 papers · 1 filter
Global existence of strong solutions to a groundwater flow problem
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system $Δv= u_{x_1},\ u_t-\mbox{div}\left(\left((a|\mathbf{q}|+m)I+(b-a)\frac{\mathbf{q}\otimes\mathbf{q}}{|\mathb…
Regularity results for a nonlinear elliptic-parabolic system with oscillating coefficients
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system $\mbox{div}(σ(u)\nablaφ)=0,\ \ u_t-Δu=σ(u)|\nablaφ|^2$. This problem is known as the thermistor problem whi…
Global existence of strong solutions to a biological network formulation model in dimensions
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system\\ $-\mbox{div}\left[(I+\mathbf{m} \mathbf{m}^T)\nabla p\right]=s(x),\ \ \mathbf{m}_t-α^2Δ\mathbf{m}+|\mathb…
Mathematical validation of a continuum model for relaxation of interacting steps in crystal surfaces in space dimensions
Xiangsheng Xu
In this paper we study the boundary value problem for the equation $\mbox{div}\left(D(\nabla u)\nabla\left(\mbox{div}\left(|\nabla u|^{p-2}\nabla u+β\frac{\nabla u}{|\nabla u|}\rig…