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- W2368278009 abstract "We consider the following semilinear dissipative wave equations with linear memory on the unbounded domain RN {uu+δut-k(0)φ(x)△u-∫∞0k'(s)φ(x)△u(t-s)ds+f(u)=h(x),(x,t)∈RN×R+u(x,t)=u0(x,t),t≤0;ut(x,0)=tu0(x,0),x∈RN. WhereN≥3;δ,k(0),k(∞)0;k'(s)≤0,s∈R+ and u0(x,t),(t≤0) are the initial data.The energy spaceX0=D1,2(RN)×L2μ(R+,D1,2(RN)) is introduced to overcome the difficulties associated with the non-compactness of operators,which arise in unbounded domains.The estimates on the Hausdorff and fractal dimension are achieved according to an asymptotic estimate of the distribution of the eigenvalue of the characteristic equation-φ(x)△u=au,x∈RN." @default.
- W2368278009 created "2016-06-24" @default.
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- W2368278009 date "2012-01-01" @default.
- W2368278009 modified "2023-09-23" @default.
- W2368278009 title "Estimates on the Dimension of the Global Attractor for a Semilinear Dissipative Wave Equations with Linear Memory on R~N" @default.
- W2368278009 hasPublicationYear "2012" @default.
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