Global attractors for the semilinear beam equation with localized viscosity

Authors: SEMA YAYLA

Abstract: In this paper, we deal with the semilinear beam equation with localized viscosity. Under mild conditions on the viscous coefficient, we establish the well-posedness and boundedness of the weak solutions. Then we prove that the semigroup generated by this problem has a smooth global attractor in $H^{3}\left( 0,1\right) \times H_{0}^{1}\left( 0,1\right) $.

Keywords: Beam equation, Boussinesq equation, Cahn-Hilliard equation, hyperbolic relaxation, global attractor

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