非線性中立型延遲分微分方程θ-方法和單支方法散逸性

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1、θ-Dissipativityofθ-methodsandone-legmethodsfornonlinearneutraldelayintegro-di?erentialequationsCandidateSupervisorandRankGuanghuaHeProf.LipingWenCollegeProgramSpecializationDegreeUniversityDateMathematicsandComputationalScienceComputationalMathematicsTheoryandAppli

2、cationofNumericalMethodsforSti?Di?erentialEquationsMasterofScienceXiangtanUniversityApril30th,2009,,.Navier-StokesLorenz..,,..tdty(t)=?(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}.?:[?τ,0]→Cd,f:Cd×Cd×Cd→Cd,g:[0,+∞)×[?τ2,+∞)×Cd→CdAbstractManydynamicalsystemsinscienceandengineeringaredissipative.Thesesystemsarecharacteriz

4、edbypossessingaboundedabsorbingsetwhichalltrajec-toriesenterina?nitetimeandthereafterremaininside.Forexample,thetwo-dimentionalNavier-StokesequationandotherimportantsystemssuchasLorenzequationaredissipative.Inthestudyofdissipativesystemsitisoftentheasymptoticbehavior

5、ofthesystemthatisofinterest,andsoitishighlydesirabletohavenumericalmethodsthatretainthedissipativityoftheunderlyingsystem.Nonlinearneutraldelayintegro-di?erentialequationsarisewidelyinthe?eldsofbiology,medical,economics,physics,chemistryandcontroltheoryandsoon.Itisme

6、aningfultoinvestigatethetheoryofnumericalmethodsfornonlinearneutraldelayintegro-di?erentialequations.ThispaperisconcernedwiththenumericaldissipativityofnonlinearVolterrafunctionaldi?erentialequations11y(t)=?(t),where·,·denotesinnerproductand·denotesthecorrespondingno

7、rm,N∈Cd×disconstantmatrixandN<1,τ1,τ2arepositiveconstantsandhereτ=max{τ1,τ2}.?:[?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