齐次化定理及其应用

21119903Vol.21.1Mar1990JOURNALOFTAIYUANUNITERSITYOFTECHNOLOGY1,:==,=()(),;;l:,,;.1;,=(x,,Al;,A:1,Alx:,xZ,,2,x,t;:)r:A0,+;Al+;Dx;(t,,oo+oo,=l,2,,)l!::=o(=o,1,2,,2)!:=f(1,2,,n,!IJI,(X!,2,,X,I:(Xl,XZ,:),x,t;:)d:(1)=;+Al.++,,D++f(1D{:=oXZ,,Xn,(jo,1t)(t)o,(+0o,=1,2,,n)2,,m1)!l.es.r.:(1),19881230.D{u=D{(x,,n,;,)+{:D,(Xl,990,x,t;d:(j=1,2,,1)D(xl,,x,t;:)d:!J”d.Tt{(1,XD==D(1,Xn,(/1,!:*+,Wdr+!AId:J.,Dj(,,)+,:+Al+.+,_,Dx.u+A::i1DI},(j,1,2,,1)(1)(1,x,t)(l)2~(x,;:)DID,++{{(t:,x){D{j,0(j0,1,2,2)}Dl,_,=(x.{{o((Dxa){o,a)O)(1),1,Ax),(x,)!(,;r)Jr(2(PZ)DD,D+Jf(x,t)(to,o()D1ul=O(jO,l,2,,l)ul=0((Duau)}=o,a)o):(2DI),D/,;)+D,(X,;)dJ:D,(/,,;)(,,,2,,:)D:D:(/,;){:D:(/,;)d(/,)+!{AdJ:And/(,t)AD+AD1ul(i==o,z,2,,1)=J:0,;,O((Da)!D(0,;)(,;)d(2),t)(,)(2)3a,(x,t;:)D.2+2no({l,2,3,},ox1.t:))jx,,00,,,Zn1)}Of(x,:),(x,t){:W(X,;r(3u+auf(x,)({,,2,:,}(P3)Duf,:=0(!t=oDou!=o0xl,to)i=o,1,2,j,Znr):(3),D:(,,;,)+J:D(,;)d{:Dt(,;D:!,;)+1:D:(X,;)d,(X,)+D,(X,;,d=f(x,t)aZD(3)(,t)(3),1,2,,2l,Du!u!,=,1J:D,j,;,dDu(3)(x,t)(3)4a,(x,t;:)(3)lpO=a(t:,0It!=o(i{o,l,2,,,{o,1,2,}),Zn})t!,=:0=f(x,:),X,,{:(X,d:(4)(;);0a+nu+j(x,t),ul,,=o({oo,Dou!:==o(to,2oxl,n{0,z,2,}),Zn});(4),D!(X,;)+{:D!(X,;)d{:DtX,;rD:D!(/,;,)+:X,;)d:f,)+!:df(,t)+aD+u({o,1,2,})D!,1D!,!d(0,,2,uoD:ul=o()21u=u+f(t)(t)o,fe){ulo=o(j=o,1,2,3)1,t;~(t:)1:=o(i=o,1,2)!:f(:)l1d,,;,_4(:)Zs(t:)7(,){z(:):(i(:)1:.JOLJ2,u=Du+j(,t)(t)o,o(+)Dtu(fDf,f(o,t)=o).(o)(to)a,jeaXZ(0,+0o),t,f=DuID2,(x,t;r)=D(t:,o)I:=f(x,,)1=0,X,)X,;)d,{I=(x)rt0,0ox+OO(0oxoo)(x,t);+0o(xp)2~l(p)-dp.tJ....r,PZ.W(x::)2(tr)(xp)2e+e1,4Jap(x,t)~{iQOJ02(tT)Joj(p,:)(xp)2(x+p)2e+e(:)!pd3{4,1DoZuaZDuEsn51not(oxl,to)(A){}~!=u{xz=04,(xD,u!,0t;.)(2a2o(t:,oxl)o=0,t:O,{=oDt1:=Esin-5Inr.,u(x(A)(x,,,)!:%,;,dt;:),(B)(x,t;:)(,t;:)=Tk(t,:)k.0ksn1x(B),,+2TkSO8,,.kZ2a2kllzk=,k(t,:)Ck(:)COS+()S,nhaes,r(t;,0Ck()+Dk()S8x(B),C(,Sx{ES,nSD*()()SnX,Ck(:)=OD,(:)Esi:.aD(:)=o(2,s,)(x,t;=ESnskn~we(A)(,,)(s;:sJaksn~--xdl2a2(sna(lsn),n4rDu=a,uhu+f(x,t)(to,ocx+oc,h0)(x,o(ocx+)(f,Df;a,feax(oc,+oc);t(o,f==o)l,(,t;:)=h(tr,OCxOC)}tl(,r)(ocx+oc),,){{(X,;)d(1,(X,;,{00j(p,:)2a(t:)(t,+-l,dP5li(t,)+ff+f(P,)ux,).1fJo,0Oa)(xp)24a2(t)dpdr{D,D{=j(r,t)(r=++0,t)o)(A)(fC(:),lC(t);t(o,f)2,(r,t;:)e.D,2+D,D,2=Q(:,,o)(B)r)}:=0D!.:j(:,/!l|J.11\,(A)U(x)(,;,d3,(:,t;:)t:OV(:,t;:)=o:0tr(r,r(r,;,{:t:,r+traf(a,r)dartrt:,rt:,(:,,;:)Jt+raj(a,datrO(t(:,t:(:,,:,1(r+,,r)JJr+:J)tr,(,Itrltrr2af(a,:)dad:tr.(t1r+tr,,.J::t+:,)a32,,BM,A,AH..:,1982328~330AH,AA;..:,1961:.62~65eoPsooET.Partialdifrerentialeqoations.London.Cambridgeuniversity,l5:2.tHomogeneousTheoremanditsApplieationChaShizhen.ZhangBaoyuzhengYuAbstract4homogeeoustheoromsonsolvingthedefiniteproblemsofnon-homogeneous11neardifferentiatingequationaresummerizedandimPro-ed.Examplesarealsogiventoshowthe;:sabilityandgeneralizationoftheProsentedresultKeywordsnonhomogeneity;homogeneoustheorem;differentiat1ngequatlon