The Initial Boundary Value Problem Of Generalized Kawahara Equations On Bounded Intervals

The initial boundary value problem of generalized Kawahara equations on bounded intervals is considered.The uniqueness and existence of the global regular solution to the problem are established by a prior estimate with the help of the energy method,inequality techniques,embedding theorem and contracting mapping principle.Under some stronger condition of the initial data,the estimates of the global regular solution is independent of bounded intervals is obtained with the help of the inequality techniques on bounded intervals.At the same time,the only weak solution is obtained on bounded intervals.The main contents of this thesis are summarized as follows.The first part of this paper focuses on the research background and methods,then the main research results of this paper are given.The second part of this paper focuses on the global regular solution which is related with interval length.First some basic definitions are given,including the working space;and then the lemma of Theorem 1.1 is given;At last by Banach fixed point theorem and priori estimates prove the global regular solution of the generalized Kawahara equation.The third part of this paper focuses on the global regular solution is independent of interval length.First of all,a priori estimate of the solution of generalized Kawahara equation is calculated that independent of interval length under the condition of the initial condition of theorem 1.1 is strengthened.Then the generalized Kawahara equation is obtained the global regular solution which has nothing to do with interval length by the inequality techniques on bounded intervals.The certificate is the only one that exists.At last the generalized Kawahara equation has a unique weak solution on bounded intervals is proved by density.