简介：Infiniteelementanalysisoftransienttemperaturefield,itisquitenotoriousthatthenumericalsolutionmayquitelikelyoscillateand/orexceedtheredsonablescope,whichviolatesthenaturallawofheatconductionForthisreason,weputforwardtheconceptoftimemonotonyandspatialmonotonyandthenderiveseveralsufficientconditionsformonolonicsolutionsintimedimensionfor3-Dpassiveheatconductionequationswithagroupoffinitedifferenceschemes.Forsomespecialboundaryconditionsandregularelementmeshes,thelowerandupperboundsfor△t/△x~2canbeobtainedfromthoseconditionssothatreasonablenumericalsolutionsareguaranteed.Spatialmonotonyisalsodiscussed.Finally,thelumpedmassmethodisanalyzed.Wecreativelygiveseveralnewcriteriaforthefiniteelementsolutionsofaclassofparabolicequationrepresentedbyheatconductionequation.

简介：为semilinear的起始边界的值问题的答案的空间腐烂在易于侧面的边界上的零个条件的可变剖面图的半无限的柱体的寓言的方程被调查。秒顺序显示出空间腐烂O的微分不平等(exp(z2/(4(t+t0))))为L2p，答案的代表性的措施被获得。导致生长或腐烂的一阶的微分不平等也被导出。在生长的情况中，为在空间的发作的上面的界限被获得，当在腐烂的情况中为全部的精力的上面的界限以数据被获得时。

简介：Thispaperdealswiththeproblemontheperiodicsolutionforthesingularlyperturbeddifferentialequationsofparabolictypeoriginatingfromchemicalkineticsinstratifiedmedia,Auniformlyvalidasymptoticsolutionisconstructedandtherelatedasymptoticestimateisgiven.

简介：Theinverseheatconductionproblem(IHCP)isaseverelyill-posedprobleminthesensethatthesolution(ifitexists)doesnotdependcontinuouslyonthedata.Butnowtheresultsoninverseheatconductionproblemaremainlydevotedtothestandardinverseheatconductionproblem.SomeoptimalerrorboundsinaSobolevspaceofregularizedapproximationsolutionsforasidewaysparabolicequation,i.e.,anon-standardinverseheatconductionproblemwithconvectiontermwhichappearsinsomeappliedsubjectaregiven.

简介：AhighlyefficientH1-Galerkinmixedfiniteelementmethod(MFEM)ispresentedwithlineartriangularelementfortheparabolicintegro-differentialequation.Firstly,somenewresultsabouttheintegralestimationandasymptoticexpansionsarestudied.Then,thesuperconvergenceoforderO(h2)forboththeoriginalvariableuinH1(π)normandthefluxp=uinH(div,π)normisderivedthroughtheinterpolationpostprocessingtechnique.Furthermore,withthehelpoftheasymptoticexpansionsandasuitableauxiliaryproblem,theextrapolationsolutionswithaccuracyO(h3)areobtainedfortheabovetwovariables.Finally,somenumericalresultsareprovidedtoconfirmvalidityofthetheoreticalanalysisandexcellentperformanceoftheproposedmethod.