Existence Of Attractors For The Kirchhoff Type Equation With Dissipating And Damping Terms

The Kirchhoff type equation was first proposed by Kirchhoff as an existence of the nonlinear wave equation for free vibration of elastic strings. The equation has great applications in many fields, such as non-Newtonian mechanics, cosmology and astrophysics,plasma problems and elasticity theory, so the study of this kinds of equations has a profound practical significance.In the paper we will study the following Kirchhoff equation with dissipating and damping terms In the initial conditions and boundary conditions the existence and uniqueness of the generalized solution and the existence of global attractor for the system. Where Ω denotes an open bounded domain of R2with smooth boundary,) satisfies both of them are given functions, the nonlinear function and for any s≥0,satisfyingThis paper is organized as follows:In the first chapter, we briefly introduce the present research situation of the Kirchhoff equation;In Chapter2, we gave some important concepts, lemmas and explained part of the functions space;In Chapter3, we used Galerkin method to show the existence of the global solution of the problem;In Chapter4, based on semigroup theory, we proved the existence of the whole attractor of the problem;In Chapter5, for this article, we did some summaries and made some prospects for the future of the equation.