简介：ＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳＷＩＴＨＢＯＴＨＮＯＮ－ＣＯＮＶＥＸＩＴＹＮＯＮＬＩＮＥＡＲＩＴＩＥＳＡＮＤＳＴＲＯＮＧＤＥＧＥＮＥＲＡＣＹＹｉｎＪｉｎｇｘｕｅ（尹景学）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔ...

简介：Theauthorsstudyaporousmediumequationwitharight-handside.TheoperatorhasnonlocaldiffusioneffectsgivenbyaninversefractionalLaplacianoperator.ThederivativeintimeisalsofractionalandisofCaputo-type,whichtakesintoaccount'memory'.TheprecisemodelisD_t~αu-div(u(-Δ)~(-σ)u)=f,0<σ<1/2.Thispaperposestheproblemover{t∈R~+,x∈R~n}withnonnegativeinitialdatau(0,x)≥0aswellastheright-handsidef≥0.Theexistenceforweaksolutionswhenf,u(0,x)haveexponentialdecayatinfinityisproved.ThemainresultisH¨oldercontinuityforsuchweaksolutions.

简介：Inthispaper,aboundaryfeedbacksystemofaclassofnon-uniformundampedTimoshenkobeamwithbothendsfreeisconsidered.Alinearizedthree-leveldifferenceschemefortheTimoshenkobeamequationsisderivedbythemethodofreductionoforderonuniformmeshes.Theuniquesolvability,unconditionalstabilityandconvergenceofthedifferenceschemeareprovedbythediscreteenergymethod.Theconvergenceorderinmaximumnormisofordertwoinbothspaceandtime.Thevalidityofthistheoreticalanalysisisverifiedexperimentally.