2024/04/04 by Kelei Wang, Wang, Kelei, Guangzeng Yi +1 · 1 citation
Computer Science · Engineering · Mathematics · #35B44 #35B45 #35K58 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computer science #FOS: Mathematics #Materials science #Mathematical analysis #Mathematics #Microelectromechanical systems #Nanotechnology #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2404.03223
openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first in a series of papers devoted to the blow up analysis for the quenching phenomena in a parabolic MEMS equation. In this paper, we first give an optimal Hölder estimate for solutions to this equation by using the blow up method and some Liouville theorems on stationary two-valued caloric functions, and then establish a convergence theory for sequences of uniformly Hölder continuous solutions. These results are also used to prove a stratification theorem on the rupture set \u=0\.