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391120096MATHEMATICSINPRACTICEANDTHEORYVol139No111June,2009,,,3(,150025):2005,,5N5t=D52N5x2-u05N5x-kN,.:;;1:2009201208:(10671049),,(11531246),(2008)3,,,.,54.4%.,,,..,,.2005.21),1900,54.56,,69132%.,,,.,2744,,.,.128122.,,,,,7,57.16.939,18164.,,123,300ö,79,2300ö.2)120051113,.,(),.,,.1410,10,.5,.,.,,,20051123,.,(16)24180.4417ö,25;190.5177ö,29.45;250.5805ö,33.15,,.3),,,.,,.,,,.,,,..,,,,,,.,,.3,,,.,,50111,:,..:5N5t=D52N5x2-u05N5x-kN,-x,t0N(x,0)=MD(x)=,x=00,x0-D(x)dx=1limxN(x,t)=limx5N(x,t)5x=0,t0(1)N(mgöL);t(h);D(km2öh);x(km);u0(kmöh);k(h-1).D(x)D,Da,Da(x).5N5t=D52N5x2,Fick(flux)5N5x,()-kN,.,.,0.4:5N5t=D52N5x2(2)(dilationscaling):N(x,t)KAN(KBx,Kt),A,B,K0.(2)N(x,t)=KAN(KBx,Kt).K=t-1,V(y)=N(y,1),y=t-Bx,N(x,t)=t-AN(t-Bx,1)=t-AV(y)(3)(2)At(-A+1)V(y)+Bt(-A+1)yV(y)+Dõt-(A+2B)V(y)=0A=B=12,2DV(y)+yõV(y)+V(y)=0.(2DV(y)+yõV(y))=0,2DV(y)+yõV(y)=a().limyV(y)=limyV(y)=0,2DV(y)+yV(y)=0.V(y)=bõe-y24D.(3)A,BN(x,t)=t-12õV(xõt-12)=bõt-12õe-x24Dt(x,t)=12PDte-x24Pt,-x+,t060139(2).[5](46)+-(x,t)dx=1.,5N5t=D52N5x2,-x+,t0N(x,0)=MD(x)=,x=00,x0N(x,t)=M2PDtõexp-x24Dt(4):5N5t=D52N5x2-u05N5x,-x+,t0N(x,0)=MD(x)=,x=00,x0-D(x)dx=1(5)z=x-u0t,s=t,W(s,z)=N(x,t),5W5s=D52W5z2,-z+,t0W(z,0)=MD(z)=,z=00,z0-D(z)dz=1(6)(4)W(s,z)=M2PDsõexp-z24Ds(5)N(x,t)=M2PDtõexp-(x-u0t)24Dt(7):N(x,t)=exp(-kt)õM2PDtõexp-(x-u0t)24Dt(8)(1),(8)(1).,N(x,t)=M2PDtõexp-(x-u0t)24Dt-kt(9)(1).5[8],,,u003.0kmöh,D04.010km2öh,k04.010-4h-1.,,.,,.70111,::[1]Banks,RobertB.GrowthandDiffusionPhenomena[M].Mathematicalframeworksandapplications.TextsinAppliedMathematics,14.Springer2Verlag,Berlin,1994.[2],,,,.[M].,2003.[3],.[M].:,1996:22268.[4],,,.[M].,2005.[5]LawrenceCEvans.PartialDifferentialEquations[M].volume19ofGraduateStudiesinMathematics.AmericanMathematicalSociety,ProvidenceRI,1998.[6]ShiJunping,Reactiondiffusionequationsandmathematicalbiology[J].UndergraduateLectureNotes,2004.1293.[7]ShiJunping,SolutionsetofSemilinearEquationsWorldScientificPress,2008.[8],,.[M].:,2003.[9],,,,,.[J].,2007,27(6):8112815.SonghuaRiverWaterPollutionModelYUDa,LIUPing,SHIJun2ping,WANGYu2wen(HarbinNormalUniversity,Harbin150025,China)Abstract:ThispaperstudiestheSonghuaRiverwaterpollutioninJilinin2005.Simulatingtherapid2onsetwaterpollutiononthewaterquality,withusingthereaction2diffusionequationsmodelthepoint2sourcemodel.Andcometoanalyticalsolution.Keywords:Reaction2diffusionequations;SonghuaRiverwaterpollution;point2sourcemodel80139