简介：1.IntroductionInthispaperweconsidertheCauchyproblemforthefastdiffusionequationwheremaxandpositivefunction.Thistypeofequationhasbeenextensivelystudiedasamathematicalmodelofalotofphysicalproblems(see[1-3]).Amajortopicofstudyistheexistenceandnonexistenc...

简介：在这，在那里的纸被建立整体存在并且有限timeblow起来下列抛物线的系统u_t=Δu+v~p的非否定的答案结果(x_0，t)-au~r,x∈Ω，t>0，v_t=Δv+u~q(x_0，t)-bv~s,x∈Ω，t>在x_0∈Ω是一个定点的地方，0使条件和非否定的原始数据遭到到homogeneousDirichlet，p，q，r，s≥第1a一，b>0个are常数。处于状况什么时候非否定的答案(u，v)上面，问题在有限时间骤起，发作是全球的，这不同于本地来源盒子，这被显示出。

简介：For2<γ

简介：Inthispaper,weconsidertheformationofsingularityfortheclassicalsolutionstocompressibleMHDequationswithoutthermalconductivityorinfinityelectricconductivitywhentheinitialdatacontainsvacuum.Weshowthatthelifespanofanysmoothsolutionwillnotbeextendedto∞,iftheinitialvacuumonlyappearsinsomelocaldomainandthemagneticfieldvanishesontheinterfacethatseparatesthevacuumandnon-vacuumstate,regardlessthesizeoftheinitialdataorthefarfieldstate.

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简介：Inthispaper,weconsiderthefollowingchemotaxismodelwithratio-dependentlogisticreactiontermu/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：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.

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简介：我们为Davey-Stewartson系统学习发作答案(D-S系统，为短)在L<潜水艇class=“a-plus-plus”>x<啜class=“a-plus-plus”>2(<啜class=“a-plus-plus”>2)。首先，我们给D-S系统的解决方案的非线性的侧面分解。然后，我们证明最小的集体发作答案的存在。由使用最小的集体发作答案的特征，最后，我们获得限制侧面和L的精确集体的集中<啜class=“a-plus-plus”>D-S系统的2个发作解决方案。

简介：Inthispaper,weconsidertheblow-upofsmoothsolutionstothe3DidealMHDequations.Let(u,b)beasmoothsolutionin(0,T).Itisprovedthatthesolution(u,b)canbeextendedaftert=Tif(↓Δ×u,↓Δ×b)∈L^1(0,T;B∞，∞^0).ThisisanimprovementoftheresultgivenbyCaflisch,Klapper,andSteele.

简介：作者为海军司烧方程学习光线的答案到一个模型方程。如果，模型方程有自我类似的单个答案，这被显示出5≤n≤9。如果起始的数据是光线的，答案将骤起，这也被显示出，足够大并且n≥5。

简介：Thispaperdealswiththeblow-uppropertiesofpositivesolutionstoadegenerateandsingularnonlocalparabolicequationwithweightednonlocalboundaryconditions.Underappropriatehypotheses,theglobalexistenceandfinitetimeblow-upofpositivesolutionsareobtained.Furthermore,byusingthepropertiesofGreen'sfunction,wefindthattheblow-upsetoftheblow-upsolutionisthewholedomain(0,a),andthisdiffersfromparabolicequationswithlocalsourcescase.

简介：Inthisnote,wewillgiveanewproofoftheblow-upcriterionofsmoothsolutionstothe3Dincompressiblemagneto-hydrodynamicequationsbyasimpleapplicationofGagliardo-Nirenberg’sinequality.

简介：Inthisarticle,weconsideratwo-componentnonlinearshallowwatersystem,whichincludesthefamous2-componentCamassa-HolmandDegasperis-Procesiequationsasspecialcases.Thelocalwell-posedessforthisequationsisestablished.Somesufficientconditionsforblow-upofthesolutionsinfinitetimearegiven.Moreover,byseparationmethod,theself-similarsolutionsforthenonlinearshallowwaterequationsareobtained,andwhichlocalorglobalbehaviorcanbedeterminedbythecorrespondingEmdenequation.

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简介：在这篇论文，我们与非线性的边界条件调查强烈联合的非线性的抛物线的系统的积极解决方案:[图形]在函数上的适当假设下面一，b，g，h，d和f，我们获得解决方案可以全球性存在或由利用上面、更低的解决方案技术在有限时间骤起。

简介：ＢＯＵＮＤＥＤＮＥＳＳＡＮＤＢＬＯＷＵＰＦＯＲＴＨＥＧＥＮＥＲＡＬＡＣＴＩＶＡＴＯＲ－ＩＮＨＩＢＩＴＯＲＭＯＤＥＬＬｉＭＩＮＧＤＥ（李名德）；ＣＨＥＮＳＨＡＯＨＵＡ（陈绍华）；ＱＩＮＹＵＣＨＵＮ（秦禹春）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃ...

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。

简介：本文用上、下解的方法讨论了一个推广的核反应数学模型的解的存在性及在有限时刻爆炸（ｂｌｏｗ－ｕｐ）的问题．