36 citations · 40 across the 11 of their papers we have counts for
5 papers · 2 filters
Existence Theorems for a Fourth-Order Exponential PDE Related to Crystal Surface Growth
Brock C. Price, Xiangsheng Xu
In this article we prove the global existence of a unique strong solution to the initial boundary-value problem for a fourth-order exponential PDE. The equation we study was origin…
Blow-up time of strong solutions to a biological network formation model in high space dimensions
Xiangsheng Xu
We investigate the possible blow-up of strong solutions to a biological network formation model originally introduced by D. Cai and D. Hu \cite{HC}. The model is represented by an…
Strong solutions to a fourth order exponential PDE describing epitaxial growth
Brock C. Price, Xiangsheng Xu
In this paper we prove the global existence of a strong solution to the initial boundary value problem for the exponential partial differential equation $\partial_tu-Δe^{-Δu}+e^{-Δ…
Existence and incompressible limit of a tissue growth model with autophagy
Jian-Guo Liu, Xiangsheng Xu
In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existe…
Partial regularity for an exponential PDE in crystal surface models
Xiangsheng Xu
We study the regularity properties of a weak solution to the boundary value problem for the equation in a bounded domain , where $ρ=e^{-\mbox{div…