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1.
Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources   总被引:1,自引:0,他引:1  
§ 1.Introduction ThispaperisconcernedwiththetimeperiodicsolutionsoftheporousmediumequationswithweaklynonlinearsourcesandwiththeDirichletboundaryvaluecondition ,namely ,theproblem u t =Δ(|u|m- 1u) +B(x ,t,u) +f(x ,t) inΩ×R ,(1 .1 )u(x ,t) =0 on Ω×R , (1 .2 )u(x ,t+ω) =u(x ,t) in Ω×R ,…  相似文献   

2.
Considerthefirstinitial boundaryvalueproblem u t=div q( u) ,  (x,t) ∈QT,(1 )u(x,t) =0 ,  (x,t) ∈ Ω× (0 ,T) ,(2 )u(x,0 ) =u0 (x) , x∈Ω ,(3 )whereΩisaboundeddomaininRNwithsmoothboundary Ω ,QT=Ω× (0 ,T) , q = φ ,φ∈C1(RN) ,and φ , qsatisfythestructureconditions(λ|ξ|1+δ-1 ) +≤ φ(ξ) ≤Λ|ξ|1+δ+ 1 ,  ξ∈RN,(4 )| q(ξ) …  相似文献   

3.
§1.IntroductionandMainResults  WeconsidertheHamiltoniansystems¨q-L(t)q V′(t,q)=0,(HS)where(t,q)∈R×RN,¨q=d2dt2q,V′(t,q)denotesthegradientofV(t,q)withrespecttoq,andthesymmetricmatrixL(t)isassumedtosatisfy:(L)L(t)∈C(R,RN2)andthereexistsλ>0suchthatL(t)x·xλ|x|2,(t,x)∈R×RN.Weassum…  相似文献   

4.
§ 1.Introduction Inthispaperwestudythestrongandweakpropertyoftravellingwavefrontsolutions (TWFS)forthefollowingdegenerateparabolicequation : ψ(u) t = 2 u x2 +f(u) . ( 1 .1 ) Welookforsolutionsof( 1 .1 )oftheformu(x,t) =q(x -ct) (cisthewavespeed) ,whereq( ξ) ,ξ=x -ct,asafunctionofas…  相似文献   

5.
1 IntroductionInthispaper,weconsiderthefollowingperiodicinitialvalueproblemforthesystemofGinzburg LandauequationscoupledwithBBMequations:x∈Rεt+ με-(α1+iα2 )εxx+ (β1+iβ2 ) |ε|2 ε-iδnε=g1(x) ,(1 .1 )nt+ f(n) x+λn-αnxx-nxxt+ |ε|2 x =g2 (x) ,(1 .2 )ε(x+ 2π ,t) =ε(x ,t) ,n(x + 2π ,t) =n(x ,t) ,(1 .3)ε(x ,0 )…  相似文献   

6.
Lagrange Interpolation on a Sphere   总被引:1,自引:0,他引:1  
§ 1.Introduction LetnbeanonnegativeintegerandS ={(x ,y ,z)∈R3 |x2 + y2 +z2 =1 }betheunitsphereinR3 .P( 2 )n andP( 3 )n denotethespaceofallbivariatepolynomialsoftotaldegree≤nandthespaceofalltrivariatepolynomialsoftotaldegree≤nrespectively ,i.e .P( 2 )n =∑0≤i+j≤naijxiyj|aij ∈R ,P( 3 …  相似文献   

7.
§ 1.ProblemandAssumptions Thispaperdealswiththesolutionsofthefollowingdifferentialinclusionproblem :Au∈f(x,u) ,x∈Ω ;u=0 ,x∈ Ω ,(1 )whereAu(x) =-∑Ni=1Di[ai(x ,Du(x) ) ] ,Ω RNisaboundeddomainwithpiecewiseLipschitzboundary Ω ,Du =(D1u ,D2 u ,… ,DNu) ,Diu = u xi,i=1 ,2 ,… ,N ,andf:Ω×R→ 2 Risa…  相似文献   

8.
§ 1.Introduction Letabeameasurablefunction ,bea φ∈S(R)nonnegativefunction ,and 0 <r <∞ .Definecommutatorsasfollows :Cra( f) (x) =supx∈Q1|Q|∫Q|a(x) -a( y) |r|f( y) |dy ,( 1 .1 )andΦra( f) (x) =supε>0∫Rn|a(x) -a( y) |rφε( |x- y|)|f( y) |dy ,( 1 .2 )whereQdenotesacubeandφε(t) =1εnφ tε .Thesetwooperat…  相似文献   

9.
§ 1.Introduction Sincesecondorderellipticboundaryvalueproblemshavewideapplicationsinphysics ,thestudyofpositiveradialsolutionsforthesemilinearproblem  (P) Δu(X) +g( |X|)f(u(X) ) =0 , R1<|X|<R2 ,u(X) =0 ,  |X|=R1or |X|=R2(whereR1>0 ,X∈Rn,n≥ 2 )hasbeenmadeforrecent 2 0years ;see [1— 5]forr…  相似文献   

10.
§ 1 IntroductionWeconsiderthefourthordersemilinearsubellipticboundaryvalueproblemΔ2 Hu +cΔHu =f( (z ,t) ,u) inD ,u|D =ΔHu|D =0 ,( 1 .1 )whereDisaboundedopensubsetoftheHeisenberggroupHnandΔHisthesubellipticLapla cianonHn.WerecallthatHnistheLiegroupwhoseunderlyingmani…  相似文献   

11.
§ 1.BasicConcepts Throughoutthispaper,A =A0 A1isalwaysassumedtobeanassociativesuperalgebrawithunityoverafiledF ,andL =L0 L1aLiesuperalgebraoverF .If |x|occursinsomeexpression ,thenitisassumedthatxisahomogeneouselementaboutZ2 gradedand |x|denotestheZ2 gradeddegree…  相似文献   

12.
§ 1.Introduction Forthewell knownBernsteinpolynomialBn(f;x) = nk=0f kn pn,k(x) , pn ,k(x) =nk xk( 1 -x) n-k,BerensandLorentz[1]provedthatforf∈C[0 ,1 ] ,0 <α<2 ,onehas| (Bnf-f) (x) |=O x( 1 -x)nα/ 2 ω2 (f;t) =O(tα) . ( 1 .1 )Ontheotherhand ,DitzianandTotik[2 ]obtainedthatforf∈C[0 ,1 ] ,0 <α<2 ,onehas| (Bnf -f)…  相似文献   

13.
梁保松  叶耀军 《数学季刊》1999,14(2):97-101
§1. IntroductionandResultInthisarticleweareconcernedwiththedecayofglobalsolutionoftheinitial-boundaryvalueproblemforthefollowingnonlinearhyperbolicequationutt+Au+|ut|αut=f(x,t)     inΩ×R+,(1)u(x,0)=u0(x),ut(x,0)=u1(x)  x∈Ω,(2)u(x,t)=0            (x,t…  相似文献   

14.
Considerthenon-linearsingularpartialdiferentialequationttu=F(t,x,u,xu),(t,x)∈Ct×Cnx,(1)whereu=u(t,x)isanunknownfunction,and...  相似文献   

15.
§ 1 IntroductionandresultsAProcess {W (s,t)∶(s ,t)∈R2 +}iscalledatwo parameterfractionalLevy Wienerpro cess[1,2 ] oforderαwith 0 <α <1 ,If {W (s,t)∶(s ,t)∈R2 +}isanalmostsurelycontinuous ,real valuedGaussianprocesson (Ω ,R ,p)withmeanzero ,W ( 0 ,0 ) =0andstationaryincre mentsE{W (s1,t1) -W …  相似文献   

16.
1 IntroductionWeshallconsiderthemodelformiscibledisplacementofonecompressiblefluidbyanotherinahorizontalreservoirΩ R2 ofunitthicknessdescribedbythenonlinearparabolicsystem[6]d(c) p t+ ·u =d(c) p t- · (a(c) p) =q ,(1.1)φ c t+b(c) p t+u· c - · (D(u) c =(^c -c)q ,(1.2 )u·ν =(D(u) c-cu)…  相似文献   

17.
§ 1.Introduction ForagraphGwedenotebyV(G)andE(G) ,respectively ,thevertexsetandedgesetofG ,with |V(G) | =ν(G)and |E(G) | =ε(G) .Agraphwithmulti edgeallowableiscalledamulti graph .Aplanargraphissuchagraphwhichhasanembedding μ(G)ofthegraphintheplane .IfGisaplanargraph ,weden…  相似文献   

18.
对求直线l:x =1 2ty =2 - 3t(t为参数 )与抛物线y2 =3x相交所得弦长 |P1 P2 |的问题 ,发现有的同学采用了如下解法 :将直线l的参数方程代入 y2 =3x ,整理 ,得9t2 - 18t 1=0 .其两根t1 ,t2 ,则|P1 P2 | =|t1 -t2 |=(t1 t2 ) 2 - 4t1 t2=2 2 - 4× 19=4 23.不难检验解答是错误的 ,正确的答案为|P1 P2 | =4 2 63.为什么会出现这种错误 ?这需要正本清源 ,从头说起 .大家知道 ,经过定点M0 (x0 ,y0 ) ,倾角为α的直线的参数方程为x =x0 tcosαy =y0 tsinα (t为参数 ) ( 1)( 1)式叫做直线的点斜…  相似文献   

19.
高级中学试验修订本数学第二册 (上 )第八章介绍了圆锥曲线的定义和范围 ,在解决有关问题时 ,若能灵活运用它们 ,则可事半功倍 .例 1  ( 1 998年希望杯赛题 )E ,F是椭圆x24 + y2 =1的左 ,右焦点 ,P是椭圆上的动点 ,则 |PE|·|PF|的最小值是 .解 由椭圆第二定义知 |PE|·|PF| =e| a2c-xP|·e| a2c+xP| =|a -exP|·|a +exP| =|a2 -e2 xP2 | =| 4- 34x2 P| .由椭圆范围知x2 P≤a2 =4 .∴ |PE|·|PF|min =| 4- 34·4 | =1 .例 2  ( 2 0 0 2年全国高考题 )点P( 1 ,0 )到曲线 x =t2y =2t(…  相似文献   

20.
1 IntroductionInthepaper,weconsiderthefollowingK -Sequation (forexample,see [1 ] -[3]andreferencestherein)inspacedimension≥ 3:Δ2 u+Δu+ 12 | u|2 -12 Ni=1li∫IN| u|2 dx=0 ,x∈IN,(1 )withL periodicboundaryconditions,L =(l1,l2 ,… ,lN)beingthesizeofatypicalpatterncell (alsobifurcationpar…  相似文献   

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