The Dynamics Of Nonclassical Diffusion Equations In Orlicz Spaces

A significant issue of the infinite-dimensional dynamical system is the asymptotic behavior of solutions for the partial differential equations.And there are many applications in mathematical physics,engineering,and the life sciences.Introducing and studying the dynamics of nonclassical diffusion equations in the Orlicz space are the primary object of this master’s thesis.Our main focus is on whether global attractors exist in Orlicz spaces for nonclassical diffusion equations.This master thesis is composed of three parts.In the first chapter,we mainly introduce the historical backgrounds,research situations,and applications for the global attractors of dynamical systems.In the second chapter,we recall the definition of Orlicz space and some abstract results,which will be used throughout the thesis.In the last chapter,we first prove that the equations in an Orlicz space have weak solutions.And then,we obtain the existence of bounded absorbing sets in a given Orlicz space.Finally,the existence of global attractors for the nonclassical diffusion equations in the Orlicz spaces is established.