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Global existence, asymptotic stability and blow‐up of solutions for the generalized Boussinesq equation with nonlinear boundary condition
Author(s) -
Zhang Hongwei,
Hu Qingying,
Liu Gongwei
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700350
Subject(s) - mathematics , mathematical analysis , nonlinear system , galerkin method , boundary value problem , energy method , stability (learning theory) , initial value problem , physics , quantum mechanics , machine learning , computer science
In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish firstly the local existence of solutions by standard Galerkin method. Then we prove both the global existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow‐up result for solutions with positive and negative initial energy respectively.