Global Well-posedness And Attractor For A Class Of Nonlinear Beam Equations

The paper is considered with global well-posedness and attractor for a class of non-linear beam equations:(?).where??R~N is a bounded domain with smooth boundary(?)?.f(x)is external force.??and g(u)are nonlinearities with the growth exponentand.This paper considers the subcritical case,in the concrete,(?).We prove the global well-posedness of weak solution and the solutions of beam equations are of higher regularity.The related solution semigroup exists global attractor and exponential attractor.Finally,we prove the compactness and attractiveness of finite fractal dimensions global attractor and exponential attractor in regular space.