3 citations · 3 across the 4 of their papers we have counts for
11 papers
Hölder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network
Xiangsheng Xu
In this paper we study the regularity of weak solutions to an elliptic-parabolic system modeling natural network formation. The system is singular and involves cubic nonlinearity.…
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…
Nonlinear diffusion in the Keller-Segel model of parabolic-parabolic type
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system $u_t-Δu^m=-\mbox{div}(u^{q}\nabla v),\ v_t-Δv+v=u$. This problem is the so-called Keller-Segel model with n…
Global existence theorem for a model governing the motion of two cell populations
Brock C. Price, Xiangsheng Xu
This article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth…