Open AccessAsymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities
Author(s) -
Qi Wang,
Yanyan Zhang
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021199
Subject(s) - eigenvalues and eigenvectors , mathematics , convergence (economics) , quenching (fluorescence) , steady state (chemistry) , parabolic partial differential equation , mathematical analysis , characterization (materials science) , rate of convergence , physics , computer science , key (lock) , partial differential equation , chemistry , optics , quantum mechanics , economics , fluorescence , economic growth , computer security
In this paper, we consider a family of parabolic systems with singular nonlinearities. We study the classification of global existence and quenching of solutions according to parameters and initial data. Furthermore, the rate of the convergence of the global solutions to the minimal steady state is given. Due to the lack of variational characterization of the first eigenvalue to the linearized elliptic problem associated with our parabolic system, some new ideas and techniques are introduced.