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This paper deals with initial-boundary problem for some Kirchhoff equations with source and damping terms. First, for convenience, a positive number d, the depth of potential well is defined and we obtain the asymptotic stability of global solution for our problem using the difference inequality which is proposed by M. Nakao.
The initial-boundary value problem for some nonlinear Petrovsky equation with strong dissipative term and source term is studied. Under weaker assumptions about dissipative term, the energy decay of global solutions is proved by means of the method due to M. Aassila.
The initial-boundary value problem for a class of inhomogeneous BBM equations with nonlinear term |u|??-2u is studied. For some range of parameter ?? value, The decay estimates of the global solutions for this problem are proved by means of Sobolev inequality.
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