带有声学边界条件的非线性粘弹性Kirchhoff方程解的存在性与一致衰减性.pdf

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18、)ds+a

19、ut

20、ut=

21、u

22、uΩ×(0,∞),(1.1)0u=0Γ1×(0,∞),(1.2)Z∂ut∂u(s)M(k∇uk2)−h(t−s)ds=yΓ×(0,∞),(1.3)2∂ν∂νt00ut+α(x)yt+β(x)y=0Γ0×(0,∞),(1.4)u(x,0)=u0(x),ut(x,0)=u1(x)Ω.(1.5)%,Vppp,y

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25、dσ,2Γ0ZtΦ(t)=−h(t−s)(ut(t),u(t)−u(s))ds.0U>tl^&d{,E(t)≤Ke−kt,e̺=∞.E(t)≤K(1+t)−̺,e̺∈(2,∞).:KirchhoffÆ
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28、.ii`[)4GlobalexistenceuniquenessanduniformenergydecayofnonlinearviscoelasticKirchhoff-typeequationwithacousticboundaryconditionsAb

29、stractThispaperisconcernedwiththeexistence,theuniquenessandtheuniformdecayforthesolutionofthefollowingviscoelasticKirchhoff-typeequationwithacousticboundaryconditions,Zt2q−2p−2utt−M(k∇uk2)∆u+h(t−s)∆u(s)ds+a

30、ut

31、ut=

32、u

33、uΩ×(0,∞),(1.1)0u=0Γ1×(0,∞),(1.2)Zt2∂u∂u

34、(s)M(k∇uk2)−h(t−s)ds=ytΓ0×(0,∞),(1.3)∂ν0∂νut+α(x)yt+β(x)y=0Γ0×(0,∞),(1.4)u(x,0)=u0(x),ut(x,0)=u1(x)Ω.(1.5)Thisd