2025/01/30 by Brock C. Price, Xiangsheng Xu, Price, Brock C. +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2501.18483
openalex publication_date 2025/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 matrix, which depends on the gradient of the solution. When the mobility matrix is the identity matrix there are now many existence results, however when it is allowed to depend on the solution we lose crucial estimates in the time direction. In this work we are able to prove the global existence of weak solutions despite this lack of estimates in the time direction.