vix.ing · top · new · best · stats

Asymptotic and Quenching Behavior for a family of Parabolic System with General Singular Nonlinearities

2020/07/27 by Qi Wang, Wang, Qi, Yanyan Zhang +1
Computer Science · Engineering · Mathematics · #35A01 #35B40 #35B44 #35K51 #35K58 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP #msc:35A01 #msc:35B40 #msc:35B44 #msc:35K51 #msc:35K58

paper · pdf · doi:10.48550/arxiv.2007.13357

17 pages, 1 figure

openalex publication_date 2020/07/27 · openalex created_date 2020/11/23 · arxiv created 2021/04/23 · arxiv updated 2021/04/26 · openalex updated_date 2026/07/28

Abstract

This study is concerned with a family of parabolic system with general singular nonlinearities, which is a generalization of MEMS system. To some extent, the classification of global existence and quenching according to parameters and initial data is given. Moreover, the convergence rate is also obtained. We point out that compared to single MEMS equation, new ideas and techniques are introduced in obtaining the convergence rate for system in our study. In fact, due to the lack of variational characterization for the first eigenvalue of the linearized elliptic system, the methods in obtaining convergence rate for single equation cannot work completely here.

Related