Some Problems Of Kirchhoff Type Equation With Damping Term And System Of Non-linear Equations

Using the view of stable set and unstable set and the energy method,we study local existence and global existence of two Kirchhoff type equations and blow up of system of non-linear equations .In the first chapter ,we analyse the global solution existence of a kind of Kirchhoff type equation with damping term utt- M( .By use of Galerkin method and potential well theory ,we offer the full conditions of global existence.In the second chapter,using the same way of the first chapter ,we offer full conditions of local existence of another Kirchhoff type eqation .In the third chapter ,we study system of non-linear equations ,and offer the full conditions of blow up with finite time.