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1.
IntroductionConsidertheswitchedlinearsystemwithmultipletime_delaysincontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) + Kk=1Dr(t) ,ku(t -τk) ,(1)wherex(t) ,u(t)andr(t)isdefinedasbefore ,(Ai,Bi,Di,1,… ,Di,K)|i=1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimplies (Ai,Bi,Di,1,… ,Di,K)ischosenasthesystemrealizationattimet.K <∞isthenumberoftime_delaysinthesystem .0<τ1<… <τKareKfixedtime_delays .Remark 1 Similarly ,wecandescribeswitchingpathbyintroducingswitchingsequ… 相似文献
2.
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
3.
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
4.
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
5.
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
6.
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
7.
Introduction InthispaperasymptotictheoryofthefollowinginitialvalueproblemforanonlinearKlein Gordonequationisconsidered.tt-Δ =εF(t,x,,ε),t>0,x∈R2,(0,x,ε)=0(x,ε),t(0,x,ε)=1(x,ε),x∈R2,(1)where(t,x)isarealvaluedunknownfunction,Δ=2i 相似文献
8.
1ConvexProgrammingandExactPenaltyFunction Weconsiderthefollowingconvexprogramming:(P)minf(x)s.t.x∈S={x∈Rn:gi(x)≤0,i=1,…,m}.SupposethatSisacompactset.ThusthereexistsalargeboundedboxX,suchthatS={x∈Rn:gi(x)≤0,i=1,…,m}intX.Assumethatf(x),gi(x),i=1,…,m 相似文献
9.
IntroductionAsymmetricregularizedlongwaveequation (SRLWE) 2 x2 -1 u t = x ρ+ 12 u2 , ρ t+ u x=0 (1 )hasbeeninvestigatedinRef.[1 ] .Thesystem (1 )ofequationsisshowntodescribeweaklynonlinearion_acousticwaveandspace_chargewaves.Thehuperbolicsecantsquaredsolitarywaves ,thefourconservationlaws,andsomenumericalresultshavebeenobtainedinRef.[1 ] .Obviously ,eliminatingρin (1 ) ,weobtainaclassofregularizedlongwaveequationutt-uxx+ 12 u2xt-uxxtt =0 . (2 )TheSRLWequationisexplicitlysymmetric… 相似文献
10.
The asymptotic theory of semilinear perturbed telegraph equation and its application 总被引:2,自引:0,他引:2
赖绍永 《应用数学和力学(英文版)》1997,18(7):657-662
I.IntroductionConsiderthefollowingsemilinearperturbedtelegraphequationuII-u., P'u==sj(t,x,u,ul,u,,e)(-ooo)(l.l)u(o,x)=u,(x,e)(-ooo,u=u(t,x),fuoandulsatisfycertainsmoo… 相似文献
11.
IntroductionLetf(x ,λ)beagivenpowerserieswithfunction_valuedcoefficients,i.e.,f(x ,λ) =c0 (x) +c1(x)λ+c2 (x)λ2 +… +cn(x)λn+… ,( 1 )wherecj(x)isarealorcomplexfunctionwithregardasxwhichisdefinedon (a ,b) .Supposethatf(x,λ)isanalyticasafunctionofλattheoriginλ=0 .ItisknownthatPad啨approximantmethodsareusedforobtainingthesolutionofawkwardintegralequations,andespeciallythosewhichpossessageneratingfunctionoftheform ( … 相似文献
12.
沈臻 《应用数学和力学(英文版)》2003,24(5):555-567
IntroductionForthestudyofwellposednessontheinitialorboundaryproblemsabouttheEulerequations,therearemanyimportantresultsgivenbydifferentmethodsindifferentfunctionclasses[1]- [4 ].Thepaper (Ⅰ )oftheauthordiscussedtheill_posednessoftheCauchyproblemswhichsatisfythesameconditionsoftheinitialvalueproblematthehypersurfacet=t( 0 ) +g(x) ,g(x) ≠constant,g(0 ) =0 R4,andgavetwodifferentformalsolutions[5 ].Italsogavetheformulasforcomputation .Inthepresentpaper,twokindsofillposednessoftheEulerequation… 相似文献
13.
1 IntroductionandProblemWeshallstudytheoptimalcontrolproblemsgovernedbynonlinearparabolicvariationalinequalitiesoftheformy′+Ay +β(y) ∈Bu+f(a.e .(x,t)∈Q =Ω× [0 ,t]) ,y(0 ) =y0 , ( )withthestateconstraintF(y) S ,andthecostfunctionalI(y,u) .Whereβisadiscontinuous,nonlinearandnonmonotonemulti_valuedmapping .Theoptimalcontrolproblemsofthedifferentialsystemshavebeenstudiedforalongtime.Manyscholars,suchasJ.L .Lions ,V .Barbu ,D .Tiba,andF .Mignotetal.,haveresearchedtheoptimalcontrolpr… 相似文献
14.
IntroductionIt’swell_knownthatthecomplicatedfundamentalsolution[1,2 ]forHelmholtzequationΔu(x) +k2 u(x) =0 (x∈Ω:boundedopenregioninR2 )isu (x,y) =-iH(2 )0 (k x-y ) 4,thusit’snotconvenientfornumericalcomputation .IfapplyingthesimplefundamentalsolutionofLaplaceequationu 0 (x ,y) =-ln|x-y|(2π) ,theexpressionforthesolutionofequationintheclosedregion Ωisc(y)u(y) + ∫Γu(x) u 0 (x,y) nx -u 0 (x ,y) u(x) n dsx =-k2∫Ωu(x)u 0 (x,y)dΩx.Astherightsideappearstheregionalintegrationinclu… 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.
肖海滨 《应用数学和力学(英文版)》2003,(4)
IntroductionInthispaper,weconsidertheexistenceofsolutionsoffollowingboundaryvalueproblemonreallineforLi啨nardsystem :u″-f(u)u′ g(u) =0 ,u(-∞ ) =0 , u( ∞ ) =1 ,(1 )wheref:R →Randg :R →RarefunctionsofclassC1.Amotivationforourresearchisconne 相似文献
17.
LetGbeaboundeddomaininthen-dimensionEuclideanspaceE",I
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18.
IntroductionInRef.[1 ]KannanandLockergivetheexistenceofatleastonesolutionofTy-h(t,y ,… ,y(n- 1) )y=f(t,y ,… ,y(n- 1) ) (a相似文献
19.
张健 《应用数学和力学(英文版)》1989,(8)
This paper deals with the two type of mixed problems with respect to Neumannboundary and Dirichlet boundary for nonlinear pseudo-hyperbolic equations of generalizednerve conduction typeu_1-△u_1=F(x,t,u,(?)u,u_t,(?)i_t)when the nonlinear part F(x.t,u,(?)u,u_t,(?)u_t)and the initial values satisfy someconditions,the blow-up properties of the solutions are obtained. 相似文献
20.
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