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1.
IntroductionInthispaper,anasymptotictheoryisestablishedforthefollowinginitialvalueproblemforasemilinearperturbedwaveequation :utt-Δu=εf(u ,ε) (t>0 ,x∈R2 ) ,(1 )u(0 ,x,ε) =u0 (x ,ε) (x∈R2 ) ,(2 )ut(0 ,x,ε) =u1(x ,ε) (x∈R2 ) ,(3 )where 相似文献
2.
IntroductionConsideraswitchedlinearsystemwithsingletime_delayinthecontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) +Dr(t) u(t -τ) ,(1)wherex(t) ∈Rnisthestate,u(t) ∈R mtheinput,thepiecewiseconstantscalarfunctionr(t) :R+ → 1,2 ,… ,Nistheswitchingpath ,(Ai,Bi,Di) |i =1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimpliesthat(Ai,Bi,Di)ischosenasthesystemrealizationattimet.τ >0isthefixedtimedelayincontrol.Inthispaper ,wewillstudythecontrollabilityofsystem (1) .Theone_per… 相似文献
3.
REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES 总被引:2,自引:0,他引:2
1 IntroductionandPreliminariesSupposeEisarealBanachspaceandTisaselfmapofE .Supposex0 ∈Eandxn+1=f(T ,xn)definesaniterationprocedurewhichyieldsasequenceofpoints xn ∞n=0 inE .Foranexample ,thefunctioniterationxn+1=f(T ,xn) =Tx0 .SupposeF(T) =x∈E :Tx=x ≠ andthat xn convergess… 相似文献
4.
丁协平 《应用数学和力学(英文版)》2001,22(2):160-172
IntroductionLetXandYbenonemptysetsand2 XbethefamilyofallsubsetsofX .LetT :X→Ybeasingle_valuedmapping ,A :X→ 2 Xbeaset_valuedmapping ,ψ :X×Y×X→R∪ ±∞ andf:X×Y→R∪ ±∞ betwofunctions.Thegeneralquasi_equilibriumproblemGQEP (T ,A ,ψ)istofind ^x∈Xsuchthat^x∈A( ^x) ,ψ( ^x ,T^x ,y)≤ 0… 相似文献
5.
马如云 《应用数学和力学(英文版)》1993,14(2):193-200
This paper deals with multiplicity results for nonlinear elastic equations of the type-d~4u/dx~4+π~4u+g(x,u)=e(x)(0相似文献
6.
ntroductionLetΩ R2 beaboundeddomain .Weconsiderthefollowingnon_stationarynaturalconvectionproblem :Problem (Ⅰ ) Findu =(u1,u2 ) ,p ,andTsuchthat,foranyt1>0 ,ut- μΔu +(u· )u + p=λjT ((x ,y ,t) ∈Ω× (0 ,t1) ) ,divu =0 ((x ,y,t) ∈Ω× (0 ,t1) ) ,Tt-ΔT +λu· T =0 ((x,y,t) ∈Ω× (0 ,t1) ) ,u =0 ,T =0 ((x,y,t)∈ Ω× (0 ,t1) ) ,u(x ,y ,0 ) =0 , T(x,y,0 ) =f(x,y) ((x,y) ∈Ω) ,whereuisthefluidvelocityvectorfield ,pthepressurefield ,Tthet… 相似文献
7.
刘国栋 《应用数学和力学(英文版)》2002,23(11):1348-1356
IntroductionThekthorderN rlundEulerpolynomialsE(k)v (x|ω1,… ,ωk)andBernoullipolynomialsB(k)v (x|ω1,… ,ωk)aregivenbythefollowingexpansionformularespectively[1]2 kext(eω1 t+ 1 )… (eωkt+ 1 ) = ∞v=0E(k)v (x|ω1,… ,ωk) tvv!,( 1 )ω1…ωktkext(eω1 t-1 )… (eωkt-1 ) = ∞v=0B(k)v (x|ω1,… ,ωk) tvv!. ( 2 )Clearlyt… 相似文献
8.
IntroductionThe following coupled cubic nonlinear Schr dinger equations inR2are considered:it-Δ=(||2-|ψ|2),t>0,x∈R2,iψt-Δψ=(-||2 |ψ|2)ψ,t>0,x∈R2,(1)where=(t,x):[0,T)×R2→C,ψ=ψ(t,x):[0,T)×R2→C,Δis the Laplaceoperator onR2.The e 相似文献
9.
Existence and Approximation of Solutions to Variational Inclusions with Accretive Mappings in Banach Spaces 总被引:3,自引:0,他引:3
张石生 《应用数学和力学(英文版)》2001,22(9):997-1003
IntroductionThroughoutthispaperwesupposethatXisarealBanachspace,X isitsdualspace ,〈· ,·〉isthepairingofXandX .D(T)andR(T)denotethedomainandtherangeofTrespectively .LetT ,A :X →X ,g :X→X bethreemappingsandφ :X →R∪ ∞ aproperconvexlowersemi_continuousfunction .In 1 999,th… 相似文献
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IntroductionLetC(k- 1)2π =h(t) |h :R →Ris (k -1 )_thordercontinuousdifferentiableandh(t+ 2π) ≡h(t) , C2π =h(t) |h :R →Riscontinuousandh(t+ 2π) ≡h(t) , ‖h(t)‖ =supt∈ [0 ,2π] |h(t) | , ‖h(t)‖Pk- 1 =max‖h(t)‖ ,‖h′(t)‖ ,… ,‖h(k- 1) (t)‖ , x(m) (t+ ·) (θ) =x(m) (t+θ) θ∈R (m =0 ,1 ,2 ,… ,k-1 ) .Clearly ,x(m) (t + ·) ∈C2π, … 相似文献
11.
A new approach for the computation of Hopf bifurcation points 总被引:4,自引:1,他引:3
叶瑞松 《应用数学和力学(英文版)》2000,21(11):1300-1307
IntroductionConsiderthefollowingparameterdependentnonlinearproblemf(x,λ) =0 , f:X×R →X ,( 1 )whereX=Rn,λisrealparameter,f∈Cr(r≥ 2 ) .Theoriginalproblemcouldbeasystemofdifferentialequation ,butherewewillassumethatasuitablediscretizationhasbeenmadeandtheproblemhasth… 相似文献
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丁协平 《应用数学和力学(英文版)》2000,21(6):637-644
IntroductionLetXandYbenonemptysetsand2XbethefamilyofallsubsetsofX.LetT:X→Ybeasingle_valuedmapping,A:X→2Xbeaset_valuedmappingandf:X×Y→R∪±∞beafunction.Thequasi_equilibriumproblemQEP(T,A,f)istofind^x∈Xsuchthat^x∈A(^x),f(^x,T^x)≤f(y,T^x), y∈A(^x).(1)TheQEP(T,A,f)wasintrod… 相似文献
13.
王文洽 《应用数学和力学(英文版)》2004,25(2)
IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 , 0 0 ,( 1 )withtheinitialandtheboundaryconditions u(x,0 ) =f(x) , 0 相似文献
14.
1 IntroductionandAlgorithmGivenafunctionf:Rn→Rn,whichisassumedtobecontinuouslydifferentiableinanopensetcontainingRn+,thenonlinearcomplementarityproblem ,denotedNCP (f) ,istofindavectorx∈Rnsuchthatx≥ 0 , f(x) ≥ 0 , xTf(x) =0 ,Clearly ,theNCP (f)isequivalenttothefollow… 相似文献
15.
张国初 《应用数学和力学(英文版)》1989,10(11):1039-1049
In this paper we are interested in the large time behavior of the nonlinear diffusionequationu_1=(φ(u))_xx φ(u), x∈R,t∈R~ =(0, ∞))We consider functionsφ(u)andφ(u)which allow the equation to possess travelingwave solutions.We first present an existence and uniqueness as well as some comparisonprinciple result of generalized solutions to the Cauchy problem.Then we give forφ(u)=u(1-u)(u-a)some threshold results,from which we can see that u=a is stable,while u=0 or u=1 is unstable under some assumptions,etc. 相似文献
16.
Introduction FangShaomeiandGuoBoling[1]consideredthefollowingtimeperiodicproblemof dampedcouplednonlinearwaveequations:ut f(u)x-αuxx βuxxx 2vvx=G1(u,v) h1(x),vt-γvxx 2(uv)x g(v)x=G2(u,v) h2(x),(1)whereα,β,γareconstants,andγ>0,β≠0.Undertheperiodicboundaryconditions,the authorsobtainedtheuniqueexistenceofstrongsolutionsfortheabovesystem.InthispaperweshallconsiderbifurcationbehaviorofthetravellingwavesolutionsofEq.(1)inthecaseGi(u,v)≡0,hi(u,v)≡0(i=1,2).Letξ=x-ct,u=u(x-ct),where cis… 相似文献
17.
曹显兵 《应用数学和力学(英文版)》2003,24(1):117-122
IntroductionInthispaper,westudyT_periodicsolutionsofthefollowingnonlinearsystemwithmultipledelays x(t) =f(t,x(t) ,x(t-τ1(t) ) ,… ,x(t -τm(t) ) ) ,(1 )wherex(t) ∈C(R ,R) ,fiscontinuous,f(t+T ,·) =f(t,·) ,τi(t) (i=1 ,2 ,… ,m)arecontinuousperiodicfunctionsofperiodT .AlemmaisintroducedfordiscussingtheexistenceofT_periodicsolutionofsystem (1 ) .LetXbeaBanachSpace ,considerthefollowingoperatorequation :Lx =λNx (λ∈ [0 ,1 ] ) ,whereL :DomL∩X→Xisalinearoperator,λ∈ [0 ,1 ]isapa… 相似文献
18.
IntroductionConsidertheindirectcontrolsystem x =Ax Bφ(σ) , σ =CTx ρφ(σ) ,(1 )wherex∈Rn,σ ∈R ,Aisn×nstablematrix ,BandCarendimensionalvectors,thesymbolTstandsfortransposition ,ρisaconstant,function φ(σ) :R →Riscontinuousandsatisfiesconditionσφ(σ) >0 ( σ∈R ,σ≠ 0 ) . (2 )Manyspe… 相似文献
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IntroductionIn [1 ] ,underagroupofveryextensiveconditions,SHENZu_hestudiedtheexistenceofaunique 2π_periodicsolutionofthesystemofordinarydifferentialequationsu″(t) G(u(t) ) =p(t) ,(1 )whereG :Rn →Rhasacontinuoussecondpartialderivatives,andp:R→Rniscontinuousand2π_per… 相似文献
20.
潘佳庆 《应用数学和力学(英文版)》2000,21(11):1331-1337
IntroductionThefastdiffusionequationofdivergenceformasut =(a(u)ux) x b(u) x c(u) (a( 0 ) = ∞ ) ( 1 )hasimportantphysicalbackground ,suchas [1 ] .Inrecentyears ,someresultsabout ( 1 )havebeenobtained .Forexample ,[2 ] ,[3]respectivelydiscussedtheCauchyproblemsforequation( 1 )andut=(… 相似文献