Existence Of Global Classical Solutions For A Kind Of Fourth-Order Of Nonlinear Wave Equations

This paper discuss the Cauchy problem for one kind of nonlinear fourth order wave equations.At the same time ,the introduce of function space which embody energy estimate and decay of solution,this space is used as iterative basic space. with the help of decay estimates of linear problem in some appropriate Banach space,when space dimension n satisfy some hypothesis conditions,initial value being appropriate smooth,and in some Sobolev space,norm being enough small,By simple iterative form and common condense image principle,Existence and uniques of the global classical solutions of equations are proved .