简介:Thispaperconsiderstheexistenceandasymptoticestimatesofglobalsolutionsandfinitetimeblowupoflocalsolutionofnon-Newtonfiltrationequationwithspecialmediumvoidofthefollowingform:{ut/|x|^2-△pu=u^q,(x,t)∈Ω×(0,T),u(x,t)=0,(x,t)∈ЭΩ×(0,T),u(x,0)=u0(x),u0(x)≥0,u0(x)全不等于0,where△pu=div(|△↓u|^p-2△↓u),ΩisasmoothboundeddomaininR^N(N≥3),0∈Ω,2
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.