非线性中立型延迟分微分方程θ-方法和单支方法散逸性

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1、θ-Dissipativityofθ-methodsandone-legmethodsfornonlinearneutraldelayintegro-differentialequationsCandidateSupervisorandRankGuanghuaHeProf.LipingWenCollegeProgramSpecializationDegreeUniversityDateMathematicsandComputationalScienceComputationalMathematicsTheoryandAppli

2、cationofNumericalMethodsforStiffDifferentialEquationsMasterofScienceXiangtanUniversityApril30th,2009,,.Navier-StokesLorenz..,,..tdty(t)=ϕ(t),,Cd,,N<1,τ1τ2,Lipschitz,fgReu−Nv,f(u,v,w)≤γ+αu2+βv2+ωw2,u,v,w∈Cd,g(t,θ,s)≤cs,∀t≥0,t−τ2≤θ≤t,s∈Cd,γ,α,β,ω,c,β≥0,γ≥

3、0,ω≥0.θ,θ,,,..:θ;θ;;;;.Id[y(t)−Ny(t−τ1)]=f(y(t),y(t−τ1),g(t,ξ,y(ξ))dξ),t≥0,t−τ2−τ≤t≤0.,N∈Cd×d·,··τ=max{τ1,τ2}.ϕ:[−τ,0]→Cd,f:Cd×Cd×Cd→Cd,g:[0,+∞)×[−τ2,+∞)×Cd→CdAbstractManydynamicalsystemsinscienceandengineeringaredissipative.Thesesystemsarecharacteriz

4、edbypossessingaboundedabsorbingsetwhichalltrajec-toriesenterinafinitetimeandthereafterremaininside.Forexample,thetwo-dimentionalNavier-StokesequationandotherimportantsystemssuchasLorenzequationaredissipative.Inthestudyofdissipativesystemsitisoftentheasymptoticbehavior

5、ofthesystemthatisofinterest,andsoitishighlydesirabletohavenumericalmethodsthatretainthedissipativityoftheunderlyingsystem.Nonlinearneutraldelayintegro-differentialequationsarisewidelyinthefieldsofbiology,medical,economics,physics,chemistryandcontroltheoryandsoon.Itisme

6、aningfultoinvestigatethetheoryofnumericalmethodsfornonlinearneutraldelayintegro-differentialequations.ThispaperisconcernedwiththenumericaldissipativityofnonlinearVolterrafunctionaldifferentialequations11y(t)=ϕ(t),where·,·denotesinnerproductand·denotesthecorrespondingno

7、rm,N∈Cd×disconstantmatrixandN<1,τ1,τ2arepositiveconstantsandhereτ=max{τ1,τ2}.ϕ:[−τ,0]→Cdisacontinuousfunction,f:Cd×Cd×Cd→CdisalocallyLipschitzcontinuousfunction,g:[0,+∞)×[−τ2,+∞)×Cd→Cdisacontinuousfunction,fandgsatisfyReu−Nv,f(u,v,w)≤γ+αu2+βv2+ωw2,u,v,w∈Cd,andg(

8、t,θ,s)≤cs,∀t≥0,t−τ2≤θ≤t,s∈Cd,whereγ,α,β,ω,carerealconstantsandβ≥0,γ≥0,ω≥0.Inthispaperweobtaintheresultsofdissipativityofthelinearθ