齐次化-Duhamel-原理的一般形式

(Duhamel)X(,,400047):指出了文献[1]中关于一般Duhamel原理陈述的错误,给出了关于一般Duhamel原理较严格的论述:Duhamel;:O175124:A:1001-8905(2000)01-0061-03,,,[1]64,,:DuhamelLu=f(x,t)m;w(x,t,S):Lw=05iw5tit=S=0,i=0,1,,,m-25m-1w5tm-1t=S=f(x,S),u(x,t)=Qt0w(x,t,S)dSLu=f(x,t)CauchyLu=f(x,t)m,,,:252u5t2=52u5x2+f(x,t),,/m0,,:5u5t=a252u5x2+f(x,t)2,,,/0,[1],,,:第17卷第1期重庆师范学院学报(自然科学版)2000年3月Vol.17No.1JournalofChongqingNormalUniversity(NaturalScienceEdition)Mar.2000X:1999-09-08:(1963-),,,,,P=5m5tm+Em-1j=0E|A|[m1aA,j(x,t)5j5tj5A5xAm,m1,x=(x1,,,xn)IRn,A=(A1,,,An),A1,,,AnIZ+(),|A|=A1+,+An,5Au5xA=5|A|u5xA11,5xAnnt1:Duhamel,Duhamel1DuhamelDuhamel1PDuhamel,tm,w(x,t,S)Pw=05iw5tit=S=0,i=0,1,,,m-25m-1w5tm-1t=S=f(x,S)(),u(x,t)=Qt0w(x,t,S)dSPu=f(x,t):5j5tj5Au5xA=Qt05j5tj5A5xAw(x,t,S)dS,(j=0,1,,,m-1,|A|[m1)5mu5tm=f(x,t)+Qt05m5tmw(x,t,S)dSPu=f(x,t)+Qt0PwdS=f(x,t),5ju5tjt=0=0(j=0,1,,,m-1):(1):PDuhamel,Duhamel(2),wufr,aA,j(x,t)r,(3)(),Duhamel:5(t)Xc(t)=A(t)X(t),Xc(t)=A(t)X(t)X(S)=F(S)W(t,S)=5(t)5-1(S)F(S),X(t)=Qt0W(t,S)dS=Qt05(t)5-1(S)F(S)dSXc(t)=A(t)X(t)+F(t)X(0)=0,Xc(t)=A(t)X(t)+F(t)X(t)=62重庆师范学院学报(自然科学版)第17卷5(t)5-1(0)X(0)+5(t)Qt05-1(S)F(S)dS,2Duhamel,:Pu=f(x,t)5iu5tit=0=0,i=0,1,,,m-1Bj[u]=0,j=1,,,lBj[u]=0,j=1,,,ll,utt=a2uxx+f(x,t)(0xl,t0)u|t=0=ut|t=0=0(0[x[l)u(0,t)=0,ux(l,t)+Ru(l,t)=0(t\0),B1[u]=u(0,t),B2[u]=ux(l,t)+Ru(l,t),B1[u]=0,B2[u]=0,Duhamel:Duhamel2PDuhamel,tm,w(x,t,S)Pw=05iw5tit=S=0,i=0,,,m-25m-1w5tm-1t=S=f(x,S)Bj[w]=0,j=1,,,l,Bj[w]=0,j=1,,,l,u(x,t)=Qt0w(x,t,S)dS:Pu=f(x,t)5iu5tit=0=0,i=0,1,,,m-1Bj[u]=0,j=1,,,l:[1],,1[M]1:,19891(下转87页)63第1期向长合:齐次化(Duhamel)原理的一般形式,,,,,,,[1]CISCOSYSTEMS.InternetworkingTechnologiesHandbook[M].Indianapolis,USA:MacmillanTechnicalPublish-ing,1997.(责任编辑李若溪)xxxxxxxxxxxxxxxxxxxxxx(上接63页)GeneralFormofDuhamelPrincipleXIANGChang-he(Dept.ofMathematicsandComputerSience,ChongqingNormalUniversity,Chongqing,400047,China)Abstract:AnerrorofthestatementaboutgeneralDuhamelprinciplein[1],ispointedoutandastrictstatementaboutitgiven.Keywords:Duhamelprinciple,initia-lvalueproblem(责任编辑许文昌)87第1期杨晓红:数据备份的误区及备份自动化解决方案