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math.AP2025
A Global Existence Theorem for a Fourth-Order Crystal Surface Model with Gradient Dependent Mobility
Brock C. Price, Xiangsheng Xu
In this article we study the existence of solutions to a fourth-order nonlinear PDE related to crystal surface growth. The key difficulty in the equations comes from the mobility m…
math.AP2021
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…
math.AP2020★ 3 cited
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…