两类非线性粘弹性方程整体解的存在性和衰减性估计.pdf

《两类非线性粘弹性方程整体解的存在性和衰减性估计.pdf》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、sRjZRpp>^VfR~6RxWY
:rrRl
2^:putRWv::'zv/5pu"[:zo,℄A:2012"4&t,nYWZ+WADeTR9B,V:=:X"h/

2、h$wx5GGv/WXAG#wCG:,kB[".,:
[sDRd"h/

3、hR",A~^DWA;VX,.$)91'z$Bbao.5?XW,.i$XWA?7,2XB#3,hb$)b>Xvd1.VXqU=wB0G.A1:rE,:2012"61E&t,nYWZ

4、+WAD.1'2wx5GGv/WXAG#wCG:,B:
[sDRd"h/

5、hR",A,[".,X"h/

6、hR"$.$XW,:
[sDRy,$XWG$Vd.
"Xjo.B=W:
[sDR}ÆA
auR"$X`,gR<Æ:y'$X}nG#^8,$)#[Bo<:
[sDR,nd(usn..}'mgÆA$,ndÆjo$X='.'zG.A1:rE,:2012"61E[1:zE,:2012"61E9ZrC{g!Æ#sRjZR

7、pp>^VfR~6Rxi&yu.X

8、18i=+,A*VbH$}&yu.B4U_=qu.W0fV-V.R19i=,&yu.WVb-
3)Vb-l_F,6VbVWF_F"%_FZ.2,h

9、4F&yu.W_F4
_FWVba`x%jT,hw4Fau.WY!&℄a`m/We0.#.[Vb
vw4FÆFu.W5&,{tGalerkinup"upURVWF"vBFT.#Fy-:a_mÆ,.[#VbW&.aim.[Vbw4FÆFu.W5&Zt

10、u−△u+g(t−s)△u(s)ds+u+

11、u

12、γu=0inΩ×(0,∞),ttt0u=0onΓ1×(0,∞),Z∂ut∂u−g(t−s)ds=ytonΓ0×(0,∞),∂ν0∂νut+p(x)yt+q(x)y=0onΓ0×(0,∞),u(x,0)=u0(x),ut(x,0)=u1(x)inΩ,-(γ>0,gj_ws._W5bF"hgWl?R-,#VW_F;hgWl?R-,y6Wj7vB"!svB9.i9ZrC{g!Æ#a(m.[Vbw4FÆ

13、Fu.W5&Zt

14、u

15、ρu−△u−△u+g(t−s)△u(s)ds+u+

16、u

17、γu=0inΩ×(0,∞),tttttt0u=0onΓ1×(0,∞),Zt∂u∂utt∂u+−g(t−s)ds=ytonΓ0×(0,∞),∂ν∂ν0∂νut+p(x)yt+q(x)y=0onΓ0×(0,∞),u(x,0)=u0(x),ut(x,0)=u1(x)inΩ,-(γ>0,ρ>0,gj_ws._W5bF"hgWl?R-,#VWF;hgWl?R-,y6Wj7vB"!

18、svB9.

19、UH;
3u;WSZH;XYÆBH;#uxD;k8exD.ii9ZrC{g!Æ#GlobalexistenceanddecayrateestimatesfortwoclassofnonlinearviscoelasticequationswithacousticboundaryconditionsAbstractPartialdifferentialequationswasbornintheearly18thcentury,atthattime,peoplededicatedtoresearchhowtocreate

20、apartialdifferentialequationmodelorlookforsomespecialequationsolutionorparticularsolution.Bythe19thcentury,withtherapiddevelopmentofanalysis,theresearchofpartialdifferentialequationshasundergoneamajorchange,manyimportantequations,inparticular,thenonlinearequation,toobtainthee

21、xplicitsolutionisimpossible.Therefore,theresearchofpartialdifferentialequationsgrad