Study On The Solution Of The Initial-Boundary Value Problem Of Two Classes Of Nonlinear Evolution Equations

In this paper,we mainly study two classes of nonlinear evolution equations,namely the generalized FitzHugh-Nagumo equations and nonlinear integro-differential equations.Firstly we prove the existence and uniqueness of the global solution of the FitzHugh-Nagumo equa-tion by the method of Galerkin,secondly we prove the existence of attractors of nonlinear integro-differential equations by the method of operator semigroup decomposition.The thesis contains five chapters:In the first chapter,we make a introduction.In the second chapter,we give the related concepts,important lemmas and basic as-sumptions which are used in this thesis.In the third chapter,we study the integral solution of non-autonomous Fitzhugh-Nagumo equation with external stimulation under the periodic boundary by the method of Faedo-Galerkin.In the fourth chapter,we prove the global attractors for a class of nonlinear integral differential equations on D(A)x D(A)by the method of ?-limit tight.In the fifth chapter,we summarize the full text.