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Global existence and nonexistence of generalized coupled reaction‐diffusion systems
Author(s) -
Niu Yi
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5480
Subject(s) - mathematics , semigroup , reaction–diffusion system , supercritical fluid , boundary value problem , polynomial , mathematical analysis , energy (signal processing) , physics , thermodynamics , statistics
In this paper, we consider the initial boundary value problem for a class of reaction‐diffusion systems with generalized coupled source terms. The assumption on the coupled source terms refers to the single equations and includes many kinds of polynomial growth cases. Under this assumption, the reaction‐diffusion systems have a variational structure, which is the foundation of constructing the potential wells to classify the initial data. In subcritical energy level and critical energy level, which are divided from potential well theory, the global existence solution, blow‐up in finite time solution, and asymptotic behavior of solution are obtained, respectively. Furthermore, we show the sufficient conditions of global well posedness with supercritical energy level by combining with comparison principle and semigroup theory.