Global existence,asymptotic stability and blow-up of solutions for the generalized Boussinesq equation with nonlinear boundary condition |
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Authors: | Hongwei Zhang Qingying Hu Gongwei Liu |
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Institution: | Department of Mathematics, Henan University of Technology, Zhengzhou, 450001 China |
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Abstract: | 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. |
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Keywords: | blow-up decay generalized Boussinesq equation global existence nonlinear boundary condition 35K05 35K61 35K70 |
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