简介:BOUNDEDNESSANDBLOWUPFORTHEGENERALACTIVATOR-INHIBITORMODELLiMINGDE(李名德);CHENSHAOHUA(陈绍华);QINYUCHUN(秦禹春)(DepartmentofMathematic...
简介:1.IntroductionInthispaperweconsidertheCauchyproblemforthefastdiffusionequationwheremaxandpositivefunction.Thistypeofequationhasbeenextensivelystudiedasamathematicalmodelofalotofphysicalproblems(see[1-3]).Amajortopicofstudyistheexistenceandnonexistenc...
简介:Inthispaper,weconsidertheformationofsingularityfortheclassicalsolutionstocompressibleMHDequationswithoutthermalconductivityorinfinityelectricconductivitywhentheinitialdatacontainsvacuum.Weshowthatthelifespanofanysmoothsolutionwillnotbeextendedto∞,iftheinitialvacuumonlyappearsinsomelocaldomainandthemagneticfieldvanishesontheinterfacethatseparatesthevacuumandnon-vacuumstate,regardlessthesizeoftheinitialdataorthefarfieldstate.
简介:Inthispaper,weconsiderthefollowingchemotaxismodelwithratio-dependentlogisticreactiontermu/t=D▽(▽u-u▽ω/ω)+u(α-bu/ω),(x,t)∈QT,ω/t=βu-δω,(x,t)∈QT,u▽㏑(u/w)·=0,x∈Ω,00,x∈,w(x,0)=w0(x)>0,x∈,Itisshownthatthesolutiontotheproblemexistsgloballyifb+β≥0andwillblowuporquenchifb+β<0bymeansoffunctiontransformationandcomparisonmethod.Variousasymptoticbehaviorrelatedtodifferentcoefficientsandinitialdataisalsodiscussed.
简介:在这份报纸,我们考虑下列非线性的椭圆形的问题:2u=|u|8n−4u+|u|q−1u,在里面u=u=0在∂ 上;一跳并且在Rn的光滑的领域,n∈{5,6,7}Rn,n∈{5,6,7}, ;是一个参数和q ∈]4/(n−4),(12−n)/(n−4)[q ∈]4/(n−4),(12−n)/(n−4)[。我们学习在二个点附近专注的答案。我们证明集中速度是一样的顺序和从对方的集中点的距离并且从边界被围住。为=()光滑的ringshaped开的集合,我们证实在二点专注的积极答案的存在指。最后,我们显示出那为>0,足够大,这个问题作为Ljusternik-Schnirelman范畴有至少许多积极答案。
简介:Thispaperdealswiththeblow-uppropertiesofsolutionstothesystemsut=Δu,vt=ΔvinBR×(O,T)subjecttononlinearboundaryconditionsδu/δη=v^p,δu/δη=u^q,inSR×(O,T).Itisshownthatundercertainconditionsthesolutionblowsupatafinitetimeandtheblow-uponlyoccursontheboundary.Theself-similarsolutionfortheone-dimensionalcasehasbeenstudied.Moreover,theexactblow-upratesarealsoderived.
简介:Weconsiderafinitedifferenceschemeforanonlinearwaveequation,whosesolutionsmaylosetheirsmoothnessinfinitetime,i.e.,blowupinfinitetime.Inordertonumericallyreproduceblow-upsolutions,weproposearuleforatime-stepping,whichisavariantofwhatwassuccessfullyusedinthecaseofnonlinearparabolicequations.Anumericalblow-uptimeisdefinedandisprovedtoconverge,underacertainhypothesis,totherealblow-uptimeasthegridsizetendstozero.
简介:我们在Dirichlet边界条件下面为边界和充分非线性的、一致地椭圆形的方程的连续粘性答案的内部坡度估计调查锋利的条件。当这些条件被违背时,能有在内部或在领域的边界上坡度骤起。特别地,我们比以前在更一般的生长条件下面在连续粘性答案的本地、全球的Lipschitz连续性上导出锋利的结果。当Dirichlet条件满足在时,边界附近的Lipschitz整齐允许我们预言一古典并且不仅仅在粘性意义,在分开能发生的地方。另一后果是这:如果内部坡度骤起发生,露天梯级类型解决方案能一般来说变得不连续,以便Dirichlet问题能在连续粘性解决方案的类上变得不可解。
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简介:Thispaperdealswiththeblow-uppropertiesofpositivesolutionstoadegenerateandsingularnonlocalparabolicequationwithweightednonlocalboundaryconditions.Underappropriatehypotheses,theglobalexistenceandfinitetimeblow-upofpositivesolutionsareobtained.Furthermore,byusingthepropertiesofGreen'sfunction,wefindthattheblow-upsetoftheblow-upsolutionisthewholedomain(0,a),andthisdiffersfromparabolicequationswithlocalsourcescase.
简介:Inthisarticle,weconsideratwo-componentnonlinearshallowwatersystem,whichincludesthefamous2-componentCamassa-HolmandDegasperis-Procesiequationsasspecialcases.Thelocalwell-posedessforthisequationsisestablished.Somesufficientconditionsforblow-upofthesolutionsinfinitetimearegiven.Moreover,byseparationmethod,theself-similarsolutionsforthenonlinearshallowwaterequationsareobtained,andwhichlocalorglobalbehaviorcanbedeterminedbythecorrespondingEmdenequation.